Basically the same coming of age story as evangelion.
Both involve a coming of age for the characters. And coming to self realizations of one's self. A crazy jumble of adolescent feelings, sci fi robots and just downright everyday strangeness and, while confusing at first, the both storys are wonderful.
Neon Genesis is not meant to be viewed as a mecha-centered action anime, but as a interwoven psychological case study of humans and their interactions with society. The main character Shinji has to overcome psychological barriers to mature.
Likewise, FLCL makes very subtle symbolic references, this time dealing with vices of human emotion, relationships, and the concept of "order", all in SIX episodes. The main character Naota also has to overcome psychological obstacles to mature.
If wimpy boys involved in bizarre tales of robots turning up in their life with aliens or giant creatures to fight off with mind-bending themes are your cup of tea, you're gonna love FLCL. Both of them make about the same level of sense too!
Both require story event-pasting, they don;t go in a straight line, they both need analysis to figure out what the hell is going on beyond the visible Drama or the superficial setting
Heavily symbolical and difficult to understand at face value, the tale of a young man's growth is told either by guitars or biological robots. Also, a series about characters and relationships.
Both are action dementia sci-fi mecha when a boy gets to ride in a robot that sometimes acts on his own will. In both, some girls gets attached to the main character without him even realizing. Both have the same "What the fuck just happened?" feeling. Both were made by Gainax.
Both are from the same author, have mecha piloted by troubled kids, psychological issues and a little of harem.
If you like unusual mecha fights, deep character development and original style, this show is for you.
Both are made by Studio Gainax and are higly symbolix and complex shows, which revolve around the same themes with a highly similar cast of characters, which develop throughout the runtime of the anime.
Both series are about being more mature (FLCL most than Evangelion) both have robots like
the EVA and Canti. Really good characters (females and males) Both are original and made
by Gainax studio.
Both follow similar metaphoric and symbolical levels of depth/storytelling. They are similar yet completely different. (Ying/Yang)