If you aren't turned off by the girly aspect of it (The director previously worked on Sailor Moon) Revolutionary Girl Utena is comparable to Evangelion in terms

If you aren't turned off by the girly aspect of it (The director previously worked on Sailor Moon) Revolutionary Girl Utena is comparable to Evangelion in terms of being ambitious and Avant-guard. (The movie is meant to be watched after the show. There's a fan website with a bunch of essays analyzing the show still active, there's a lot of subtle stuff going on in it, it was also partially inspired by japanese avant guarde theater in the 70s counterculture era.) I feel the dub hurts the material because the actors sound like they are doing children's theater so it's best watched subbed. Big O is also a good show though it gets better as it goes along. It gets kind of abstract and embraces a sort of "theater of the absurd" sort of atmosphere so don't go into it expecting a typical narrative to the story. If you like American superhero movies or comics at all Tiger and Bunny is a great Japanese show with a unique take on them. Puella Magi Madoka Magica was sort of described as a "deconstruction" of Sailor Moon type shows, a writer with a horror background does a grim and gritty story that starts off like a Sailor Moon sort of thing and goes somewhere else.