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Only watched Evangelion, but I'd definitely recommend you to watch Big O. It's a little tryhard regarding psychological stuff, but the atmosphere really is something else.
Most episodes have their own little story, so I'd advise you to start off with either Daemonseed, A Legacy Of Amadeus, Winter Night Phantom or Day Of The Advent, just to see if you're into it. If you liked the episode you picked, you should start from the beginning.