Evangelion, from 1980?
Tomino's version of Eva, made 15 years earlier
For all the talk about how Eva is so original, its surprising when you look back over mecha animes in the 20 years before it only to find many concepts from Evangelion already used! The similarities to Mobile Suit Gundam have already been discussed on this site. But if you go just a year later you will find an anime even more similar to Evangelion, from Yoshiyuki Tomino as well.
Beginning soon after Gundam was cancelled, Space Runaway Ideon premiered in Japanese television in 1980. Like Gundam before it, Tomino took mecha anime to new heights by continuing the mature philosophies he had in Mobile Suit Gundam. Starting on the colony planet Solo and featuring action over the entire universe, Space Runaway Ideon features the powerful mecha Ideon, piloted by young Earth colonists who are under pursuit from the mysterious Buff Clan, aliens who look identical to humans but are much more advanced than we are. Traveling across the universe on the Solo Ship, the Ideon along with refugees from Solo, where the Ideon was created flee from the Buff Clan while trying to find out as much as they can about the mysterious mecha they use and the ship they are on, left behind by a long dead civilization.
Ideon lacks the male angst featured so heavily in Gundam and Evangelion for all but a short period of time in one of the stand alone episodes, but character templates to Eva remain. Kasha Imhof, one of the pilots of the Ideon is a bloodthirsty, aggressive girl. As into the fighting as her male colleagues its often Kasha who displays the most anger and resentment in battle, similar to a red headed pilot we all know so well. Sheryl Formosa, a linguistic scholar aboard the Solo Ship who investigates the Ideon and the powerful 'Id' energy that powers it is arrogant and obsessed, similar to how Ritsuko eventually becomes as Evangelion draws to a close.
Religious symbolism is used very sparingly in Ideon, in fact there is only a few notable ones, like the use of the term 'Messiah' in the second Ideon movie, 'Be Invoked'. The Ideon itself is called a God by allies and enemies alike, and is revered as much as Eva Unit 01. It is the key to the plans of both the Buff Clan and the 'Id' energy that has a mind of its own. The Ideon, like Unit 01 goes berserk multiple times in the series displaying even more power than it appeared to have before.
The main similarity between the two shows however is the concept of Instrumentality from Evangelion, which is exactly like what occurs in Ideon. In Ideon, the powerful 'Id' energy is pursued by the Buff Clan and powers both the Ideon and the Solo Ship. The Id is no simple energy source though, it has a mind of its own and is responsible for bringing the two enemies together. It is later made clear than Id is actually the consciousness of all the people of the civilization that created the Ideon, merged into a single entity. The Id has a mind of its own and is sick with the war like nature of both planets. Humanity and the Buff Clan have multiple chances to reconcile themselves, but their war-like mentality is too entrenched and the Id, like SEELE in Evangelion decide that humanity is far too corrupt to continue living in this state. Everyone will die and be merged into a single entity, the Id itself and thus corruption, war, and the like will vanish from the universe entirely. This is the exact scenario from Evangelion with Instrumentality/Third Impact. The one difference? Ideon's instrumenality succeeds while Eva's is stopped by Shinji in End of Evangelion.
The fact that Evangelion was influenced by Ideon is something that can't be argued, Anno himself has admitted it as a major influence and even the most hellbent Eva fanatics who have seen Ideon in its entirety will admit the two are immensely similar. One final reference is made at the very end of the final episode of the TV series when the message 'And to the children, Congradulations!' appears on the screen. This is referring to the very end of the Ideon: Be Invoked movie where the souls of the children who died are all singing 'Happy Birthday Dear Children'. The use of the word 'Children', so prevelent in Eva when referring to the Eva pilots is used in Ideon to refer to the souls of the dead characters after Ideon's version of Instrumentality has succeeded.