I think that Evangelion episodes 25 and 26 and episodes 25' and 26' occur concurrently; I think they show dual views of the one single story thread.
Episode 25 follows episode 25' very closely (in pacing and theme, if not actual real events), and it should because episode 25 was based on the script for episode 25'. The images of Miasto slumped against a wall, Ritsuko floating in LCL and Asuka underwater in Eva-02 that are shown in the series ending are all glimpses into "reality", into what is actually going on in the real world. Most people generally agree that there is no great derivation between the two.
When it comes to 26 and 26' however the arguments begin. I will just state upfront now that I think the endings shown in episode 26 mirrors episode 26', that Shinji decided not to run away in both, that he decided to reject Complementation and return to reality.
I am going to quote big sections from the scripts to explain my reasoning here. This is necessary in my opinion because it pushes home the similarities between what is said in each ending, in some cases where the lines are almost identical. The following is from the end of episode 25; it sets the scene perfectly in my opinion. I will highlight the relevant lines that I think are most important and then compare them to lines said in the movie ending.
(The stage is illuminated)
SHINJI: What the hell is this??
MISATO: This is the Instrumentality which your father has initiated.
SHINJI: This is it?
MISATO: This is part of it.
ASUKA: You can't tell what the truth is, Shinji.
RITSUKO: Truth is subjective. Therefore, you can barely tell that what you can feel is fact.
REI: The truth is within you.
FUYUTSUKI: And the facts that remain in your memory are what will become your truth.
RITSUKO: Truth can be changed from time to time, sometimes.
SHINJI: This is all fact! This is the result of... Everything?
ASUKA: This is real; but one of many realities.
MISATO: This is the conclusion you wanted.
SHINJI: Wanted...? Me?
REI: Yes; total destruction. You wished for a world in which nobody would be saved.
SHINJI: I didn't wish for this! The others didn't save me?!
RITSUKO: Nobody can save you from yourself.
KAJI: This is what you wished for.
ASUKA: Destruction. Death. And return to nothingness. You wished for these.
MISATO: This is the reality that is.
SHINJI: What is reality...?
REI: This is your world.
HYUGA: A world that exists solely for yourself; one without time, space, or anyone else.
AOBA: A world in which every facet is determined by you.
MAYA: This is the world where you just wait for others to give you something.
That is reality.
MISATO: This is your world unless you decide to change reality.
SHINJI: This is the world that is! Nothing can change that!
RITSUKO: No. You, yourself, make the decision.
FUYUTSUKI: This is the world where your mind decides what will be.
That is reality.
MISATO: Whether it is the will to survive...
ASUKA: Or a wish for death, it is all up to you.
SHINJI: Are you saying that this darkness -- this insane world -- are what I really wished to create?!
KAJI: You wished for a closed world, that was comfortable for you.
HYUGA: You wished for it, in order to protect you from your weakness.
AOBA: To protect your few pleasures.
MAYA: This is merely a result of your wish.
MISATO: In your closed world, in a world where only you are allowed to be, others cannot live with you.
ASUKA: But still you wished to close off the world that surrounded you.
RITSUKO: Your wish ejected things you dislike, and created an isolated and lonely world filled with nothing.
REI: This is the world your wishes have created, a private haven in the recesses of the mind.
ASUKA: This is how it all ends; one of many possible endings.
MISATO: This is an ending you brought upon yourself. You chose this fate.
That sets the stage. That brings us into episode 26. Shinji is given the choice, it is made extremely clear that the choice is his; this world is of his making. It is stated more than ten times in that passage that even though this is the "Instrumentality" that was Gendou's plan, it is still Shinji's wish, his choice, his decision, for it to be this way. This mirrors very much what happened in the movie ending, it is Shinji's decision, and the fate of the world rests in his hands. Here is the scene from episode 26' that occurs just after Komm Suesser Tod starts playing, I think this shows equivalent feelings on Shinji's part, I'll juxtapose the specific lines next.
Shinji: Nobody understands me.
Rei: You didn't understand anything.
Shinji: I thought it was supposed to be a world without unpleasantness... without uncertainty.
Rei: Because you thought that everyone else was like you.
Shinji: Betrayed! You've betrayed my feelings!!
Rei: You've misunderstood from the start. You simply assumed without asking.
Shinji: Nobody wants me. So, everybody just die.
Rei: Then, what are those hands for?
Shinji: Nobody cares whether I exist or not... Nothing will change. So, everybody just die.
Rei: Then, what is that heart for?
Shinji: It'd be better if I wasn't here either. So I should just die, too.
Rei: Then, why are you here?
Note that this scene occurs just before Lilith expands her Anti-AT Field and everyone loses physical form. The "wish" of Shinji is clear to see here. Series: "KAJI: You wished for a closed world, that was comfortable for you.", Movie: "Shinji: I thought it was supposed to be a world without unpleasantness... without uncertainty. ".
The first scene I posted from episode 25 actually takes place after the second in my opinion. In the second we are shown that Shinji wishes for death, that he wishes everyone would just die, and immediately after that we see his wish effectively granted, that everyone loses physical form, they all revert to LCL. However he then gets the chance to ponder that decision, "Whether it is the will to survive... Or a wish for death, it is all up to you.". It is Shinji's choice, he is given it in the series ending and he is given it in the movie ending as well. And so it goes... everyone has "died"...
(Screen text: Do you feel good?)
(Three girls standing still in crowd)
Shinji (voice): I don't understand... I don't really understand reality.
Rei (voice): So, you can't understand the gap between other's reality and your own truth.
Shinji (voice): I don't know where to find happiness.
Rei (voice): So, you can only find happiness in your dreams.
(Crowded street- camera focuses on three individuals; dressed as Misato, Rei, and Asuka)
Shinji (voice): Then, this isn't reality... Because no one is here.
Rei (voice): Yes, it's a dream.
Shinji (voice): So, I'm not here either.
Rei (voice): You were trying to remake reality with convenient fantasies.
Shinji (voice): Is that wrong?
Rei (voice): You were using fabrications to escape from reality.
Shinji (voice): Can't I dream alone?
Rei (voice): That would not be a dream. It would just be compensating for reality.
(Packed theatre -> empty theatre)
Shinji (voice): Then... where is my dream?
Rei (voice): It is the continuation of reality.
Shinji (voice): Where is... my reality?
Rei (voice): It is at the end of your dream.
(Flashing Japanese text and images)
SCENE: Blood/LCL gushes from Lilith-Rei's neck as she leans backwards
Here is basically compressed version of what happens in the first part of episode 26 in my opinion, Shinji begins to realise that what he was doing (what he "dreamed") wasn't really reality, that he was just escaping from reality, he was running away. The issue of running away of explored in episode 26.
SHINJI: I mustn't run away!
REI: Tell me why you mustn't run away.
SHINJI: Because -- escaping from reality can be painful!
REI: Even though you're running from something more painful?
SHINJI: I couldn't bear it...
ASUKA: As long as you know what the pain is, it can be endured.
MISATO: That's correct. If the pain is too harsh, you can escape it.
REI: If you really hate it, Shinji, you can still run.
SHINJI: No! I won't! I'm tired of escaping! Yes -- I mustn't run away!
MISATO: That is true. That is because you are now aware that running only brings you more pain.
ASUKA: This is because running away can be far worse.
REI: That's why you do not wish to escape.
SHINJI: Because if you run away, nobody will respect you!
Shinji confirms fully here that he must not run away, he solidifies that mindset, he wont run from his problems any more. Looking back over what has previously discussed, I think it is clear that Shinji's original "wish" was just another form of "running away", he wished for "a world without unpleasantness... without uncertainty", a place of safety where he was protected, that was in effect just another form of running away.
The next scene in episode 26' is extremely important, because it is here that Shinji makes his decision, he changes his wish.
SCENE: Shinji and Rei merged together in the sea of LCL
Shinji: Ayanami... where are we?
Rei: This is the sea of LCL... The primordial soup of life. A world without AT Fields... without your own shape. An ambiguous world where it is impossible to tell where you end and other people start. A fragile world where you exist everywhere, and thus exist nowhere.
Shinji: Have I died?
Rei: No, everything has just been joined into one. This is the world you have been hoping for... your world.
Shinji: (releasing Misato's cross from his left hand) But... this isn't right. I don't think this is right.
Rei: If you wish once more for the existence of others, the barriers of the heart will separate everyone once more... And the fear of other people will begin again.
Shinji: That's all right... (disengages Rei from him and clasps her hand) Thank you.
(Shinji and Rei, Shinji's head lying in Rei's lap)
Shinji: I feel that there were only hateful things there. So I'm sure it was okay to run away. But there was nothing good in the place I ran to, either. After all, I didn't exist there... which is the same as no one existing.
Kaworu: Is it okay for AT Fields to hurt you and others once more?
Shinji: I don't mind. But, what are you two within my heart?
Rei: Hope. The hope that people might be able to understand one another.
Kaworu: And the words 'I love you'.
Shinji: But that's just pretending - a self-intoxicating belief... like a prayer. It can't possibly last forever. Sooner or later I'll be betrayed... And they'll leave me. Still... I want to meet them again, because I believe my feelings at that time were real.
Here we see the real turning point. Shinji's "wish world" is explained to him, and a number of lines are strikingly similar to ones said in episode 26. Here is a passage from episode 26 just before the parody sequence, note the underlined sections.
What is reality?
SHINJI: What is this... An empty space? An empty world? A world where nothing exists but myself? But with only myself, I have nothing to interact with! It's as if I'm here, but not here at all! It's as if I'm slowly fading out of existence...
YUI: Because only you are here.
SHINJI: Only... Myself?
YUI: Without others to interact with, you cannot truly recognize your own image.
SHINJI: My own image?
The image of myself?
MISATO: That's right! In the act of observing others, you may find, and recognize, yourself.
ASUKA: Your self-image is restrained by having to observe the barriers between yourself, and others.
REI: And yet, you cannot see yourself without the presence of others.
SHINJI: Because there are others, I can perceive myself as an individual! If I am alone, then I will be the same without others! For if this world is only of me, then there will be no difference between me and nothing!
MISATO: By recognizing the differences between yourself and others, you establish your identity as 'yourself'.
I think it is apparent when you review this scene in the context of the one from episode 26', that Shinji's "empty world" is the world without AT Fields. It is a world where the barriers between people cease to exist, there is no different between Shinji and anyone else, no difference between himself and nothing, it is the same as if he didn't exist. Here Complementation is equated with ceasing to exist.
At this point in episode 26', Shinji rejects Complementation. Eva-01 breaks out of Lilith's eye, Lilith collapses and the Black Moon explodes. It is quite clear that Shinji rejects complementation here in the movie, but in the series ending there is still the next step to go (which I think is also somewhat mirrored in EoE, and has to do with not just rejecting Complementation, but deciding to return to reality).
After the parody scene in episode 26 comes an extremely important sequence, so important I'll post the original Japanese here as confirmation of the translation.
SHINJI: ...I see. So this is another possibility. Another possible reality! This current 'myself' is the same way! It's not the true 'myself'! I can be any way I wish to be! I see! And 'myself' who is not an EVA pilot can exist as well!
MISATO: If you take that into consideration, then perhaps the real world isn't that bad. (Sou omoeba, kono genjitsu-sekai mo kesshite warui-monja naiwa)
SHINJI: Still... The real world itself might not be bad, but I could still hate myself. (genjitu-sekai wa, waruku-nai kamo shire-nai, demo jibun wa kiraida)
Just to note "genjitsu" = real and "sekai" = world so "genjitsu-sekai" means "real-word".
Here after "experiencing" the parody world, Shinji realises that life has many possibilities, and that Shinji as a person can exist even if he isn't an Eva pilot, and thus, as Miasto points out to him, the real world, genjitu-sekai, reality, isn't so bad after all. Shinji accepts that the real-world might not be bad, but he still hates himself. Shinji hating himself is the last obstacle; he still doesn't see value in himself. It goes on from there, the final scene.
HYUGA: But it's your mind which takes reality and separates it into what's bad and hateful.
AOBA: It is only the mind which separates reality from truth.
MAYA: The angle of view and the position from which you view your reality, will change your perception of its nature. It is all, literally, a matter of perspective.
KAJI: There are as many truths as there are people.
KENSUKE: But there is only one truth that is your truth. That's the one that's formed from whatever point of view that you choose to view it from! It's a revised perception, that protects you!
TOJI: That's true! And one can have a perspective that's far too small!
HIKARI: However, a person can only see things from the perspective that they choose to see them from.
ASUKA: One must learn to judge things via the perceived truths that one receives from others.
MISATO: For example, sunny days make you feel good.
REI: Rainy days make you feel gloomy.
ASUKA: If you are told this is so, then that is what you believe is so.
RITSUKO: But you can have fun on a rainy day, as well!
FUYUTSUKI: Your truth can be changed simply by the way you accept it. That's how fragile the truth, for a human, is.
KAJI: A person's truth is so simple, that most ignore it, to concentrate on what they think are deeper truths.
GENDO: You, for example, are simply unused to what it is to be liked by others.
MISATO: You've never learned how to deal with fearing what others feel about you, and so you avoid it.
SHINJI: But... Don't the others hate me?
ASUKA: What are you, stupid?! Haven't you realized it's all in your imagination, you mega-dork?!
SHINJI: But... I hate myself.
REI: One who truly hates himself, cannot love. He cannot place his trust in another.
SHINJI: I'm a coward. I'm cowardly, sneaky and weak!
MISATO: No. Only if you think you are. But if you know yourself, you can take care of yourself.
SHINJI: I... hate myself... but... but, maybe... maybe, I could love myself...! Maybe... My life could have a greater value...! That's right! I'm no more, or less, than myself! I am me! I want to be myself! I want to continue existing in this world! My life is worth living here!!
They show Shinji that he can have value in his life. It is that simple, that he can love and care for other people, that he has worth. Previously he accepts that the real world might not be so bad, but he still hates himself, now he realises that he doesn't have to hate himself, that his life can have value. In the end he decides to continue to exist (note that it has been previously established, by Shinji's own words, that if he accepted Complementation he would "cease to exist"), he choses to keep living, to not cease to be.
In episode 26' we see Shinji back in reality, he is on Earth, in the real world, he keeps living, he has rejected Complementation. In episode 26 we see this "dark room" blasted away, we see Shinji say he wants to keep living, he wants to exist, he is congratulated by everyone in his imaginary world (including a very dead Kaji, which should tell everyone that this scene is very much fantasy, and not some "image" of Complementation) and then with a smile, the new Shinji, the Shinji with value, disappears from our screen with a thank you to everyone.
The final text on the screen at the end of episode 26 includes a farewell to Shinji's mother, which is mirrored in episode 26' "Good-bye, mother.". Shinji returns to reality, and Yui floats away into space in Eva-01.
So there you have it, my argument for the concurrent nature of episodes 26 and 26'. I think that they both essentially show the same thing, that they both portray a boy, discovering that his life is worth living. This is a rather extended explanation of my stance and it is based solely on the series and movies endings themselves. I could have provided extra external evidence to support my position, but I didn't use them to establish this position in the first place, so I don't think they are needed now to show how I got here. I have always thought Shinji rejected Complementation, from the first time I saw the series ending oh so many years ago. The entire last sequence of episode 26 is one of triumph, of success, of revelation, it never even occurred to me that all this would happen and them *bang* Shinji would effectively cease to be. When I first saw End of Evangelion, it only served to show me the reality of what I already believed from the series.
Many people will disagree with this interpretation of the series ending, and they are more than welcome to, after all every one of us is simply trying to find our own answers.