Asking the question on a forum isn't going to give you much insight, you'll just get fanboys from both sides telling you that their console of choice is better and giving no good reason for why. You'd be better off researching each system's game catalogue on Wikipedia for the sake of impartiality.
That said: I'm an FPS-hating 360 player and have enough games to keep me amused, however they're all multi-platform (Guitar Hero, Rock Band, Skate 2 etc) so that doesn't really help much with your dilemma. If we're just talking non-FPS rather than strictly non-violent, there's some 360-exclusive RPGs that aren't necessarily about violence, though obviously there's an element of combat to them. Oh, and Viva Pinata... but that's really for kids - I don't necessarily mind cartoony games, but Viva Pinata just gave me a headache.