When I played the Xbox 360 I didn't see any groundbreaking new gameplay or ideas. It's just an updated version of the Xbox. However, it is still updated and has great graphics. I didn't get excited about the Xbox 360 though for exactly that reason.
However, the Wii is really trying something new with the controllers and I count on them to have titles that really integrate the controller to create totally new gameplay experiences. The graphics aren't as good but I think graphics have been good enough for years now.
I really don't play consoles much and havn't cared about them since I stopped playing the N64 when I was like 12.
The Wii really interests me though because it's fun to play in groups. Moreso than even normal consoles are because of the motion aspect of the game. I never play consoles alone and I got the Wii specifically for group play when friends are over because I think it's a better social console.
So, I'd say.. if you want it a console that you can play alone and get really into the virtual environments and such an Xbox 360 might be better for you. However, if you'd rather play with friends and get into the social dynamic of kicking your friend's asses then I'd get a Nintendo Wii. The xbox still offers multiplayer and the wii still offers single player but I really feel they do one area better than another.
Just buy both and return one of them while you still can for a full refund. Hell, if you could get a Nintendo Wii right now you could get $400+ easily on eBay so I'd get one if you can find it anyway.