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EL is only guilty of being a mediocre series, filled with nonsensical moments and blatant clichés, relying mostly on dark themes, like gore. Only someone who is completely obsessed with anime, or a teenager who hasn't yet recovered from heartbreaking stories in the style of "all people are jerks, how sad for the horned mutants," would seriously try to find a deeper meaning in it.
"Evangelion" wins with its very good plot, characters (the two main characters, Asuka and Shinji, are far from being my favorites), and atmosphere. But, undoubtedly, fan fiction based on "Evangelion" is a very common phenomenon and sometimes as widespread as fan fiction based on EL. The most frequently touched upon fan fiction themes are Shinji's introspection and (also common) his
subtle and complex relationship with Kaoru Nagisa (as well as Kaoru himself).
I don't really like Shinji's lengthy emotional breakdowns, and Kaoru Nagisa is just nonsense, which, unlike introspection (which is still an important part of "Eva" and can be tolerated, and both endings of the series that follow from it turned out well), should be sent to a bioreactor equipped with an anti-AT field. Fan fiction on the theme of Shinji's self-analysis (there is no deeper meaning in them than the quite complete one that lies on the surface) and
characters like Kaoru Nagisa is, of course, also epic, but it won't surpass EL.