I wasn't able to get into the Neon Genesis series, but yeah I watch anime all the time. I would have to say that Cowboy Bebop and RahXephon are my 2 top fav's, although, Trigun, Saikano, Noir and Deathnote tie for 3rd place, lol.
Have you seen the live action version of Deathnote? Its a bit different.
RahXephon is about this high school kid that is summoned to pilot some sort of huge Mecha, fighting other Mecha's. It's not lot most though, well I'm not sure but he has to make a new world or something like that, lol. I suck at explaining stuff.
You might not like it that much because these mechas are different, they're alive. All the other types of mechas I've seen are much different and are more mechanical than living. And this series of Anime is serious, not like the young/comedy anime.
I like more serious anime but I occasionally check out comedy like Trigun.