360: I own one.
Pros - Huge, awesome game selection. Pretty powerful hardware. Xbox Live online system is unrivaled and is TONS of fun. Good media features as well. I play it pretty much every day, and I love it.
Cons - Price (compared to Wii).
Wii: My best friend owns one
Pros - Fun for a while, relatively cheap, cool control scheme, great at parties, web browser is sorta nice.
Cons - Gets old, not very many good games out, controls suck if you like shooters, no real online gameplay. My friend stopped playing his after a month, he only uses it now when people are over.