I personally prefer the PS3. However the new silent 360 slim has made me enjoy it a lot recently.
Here are the main things I prefer about the PS3.
If you are owning mutiple consoles of the same kind in the same household, the PS3 easily allows you to do this. You can easily log in and out and play your digital downloads between the different logins.
Bluray player, even though I have stand alones, I like this feature.
Controller is better for beat 'em ups.
No annual fee.
Nicer interface. / photo viewer / music player / overall media center.
Overall value for money, when you take the entire package into consideration.
What I prefer about the 360....
The controller is better for racers and FPS's
More choice on XBOX live, than Playstation Network
Probably better exclusives.
I don't have any online friends, I can't be bothered with any online chat with anyone, so that isn't taken into consideration, but they say the 360 is better for all of that.