I'll keep it simple.
360 if you like multiplayer games, a very strong online system, and sports games.
PS3 if you like a multimedia powerhouse and games that force people to "grind" (mostly rpgs, strategies).
To be honest, I don't run around asking is X better than Y, but rather I buy X or Y for a specific game.
In the past, I've bought a PS2 for Gran Turismo and an Xbox for Halo. I currently don't own either of these systems, but a number of friends and family do, thus I get a good amount of playing time for each. From what I've experience, if you were a casual gamer, who just wanted a solid selection of games and a method to play with other people very easily, 360 is right up your ally. I feel this accounts for 70% of the gaming community. On the other hand, if the PS3 has the titles you're interested, or if you were to use your PS3 as a blue-ray player/folding@home/media powerhouse, then that's what you'd get. I feel that the 360 has turned into the industry standard, and the only reason to get a PS3 would be for the titles.
Personally, I'd get a PS3 since more people I know have a 360. Diversification if you will.