One of the things I don't like about anime is it con often be quite childish at times. Sometimes that's ok but sometimes it can spoil it a bit.
Anyway one anime series I watched that was quite serious was Afro Samurai.
Oh, and Neon Genesis Evangelion manages to be quite adult. It goes a bit strange and psychological in the last four episodes or so. Perhaps you'd like that, Ben.
Anyway that last one is a giant robot anime so if that's not your bag, avoid it.