I have both so I think I'm qualified to help you out.
360
Good exclusives( Mass Effect, Gears of War, the Halos,etc..) However, if you have a good PC pretty much all of these are available to you. It's also good for exclusive DLCs.
The online is payed, and you have to pay for an adaptor as well, the good news is that the service is pretty cool so you sort of get your money worth it.
It's not exactly a cheap console because you'll probably want to get an Elite which has a lower failure rate than the normal 360, making it actually more expensive than the PS3.
PS3
A very nice list of exclusives( MGS4, Demon Souls, Valkyria Chronicles, Uncharted,etc...) plus the upcoming ones like Heavy Rain and GOW 3.
The online is free and the service is pretty decent.
The new PS3 slim is sort of cheap, that's the one you should get if you end up buying a PS3. Please not that it still doesn't play ps2 games which is a bummer to be honest.
So if I were you, I'd definitely get a PS3.
Honestly, I'm much happier with it than my 360.