I own both a PS3 and a 360. Despite the reputation, the PS3 is a great console and actually has some of the best games this generation, most people just don't know it. Sony really needs to work on their marketing department because they need to get the word out.
First, the PS3 has great games, is a blu-ray player, can store music and video, and the PSN is great and free.
The 360 has great games and can do great things, especially with the New Xbox Experience. But Xbox Live is not free but the console is cheaper. Now, let's get to the games, which is probably your chief interest.
PS3 Games
Metal Gear Solid 4 (one of the best games ever)
Resistance (great FPS series with great multiplayer)
Little Big Planet (no other game like it)
Uncharted (great game, prefer it to Gears of War and a sequel is coming out)
Heavenly Sword (great action game, if short)
Folklore (interesting RPG)
Ratchet & Clank (great action and fun)
Killzone 2 (not yet released, but looks incredible)
God of War III (not yet released, but a continuation of the best action series ever)
Wipeout HD (great racing game with nice multiplayer options)
Motorstorm(good racing game)
Final Fantasy Versus XIII (still an upcoming exclusive)
Xbox Games
Halo series (excellent FPS)
Gears of War series (excellent shooter)
Lost Odyssey (good RPG)
Blue Dragon (good RPG)
Tales of Vesperia (good RPG)
Mass Effect (excellent RPG shooter from the makers from BioWare)
Fable II (good game if overrated)
Star Ocean 4 (upcoming exclusive RPG)
This list is just exclusives. They don't include multiplatform games like Call of Duty, Bioshock (one of the best FPS ever, BTW), Prince of Persia, Fallout 3, Mirror's Edge, Dead Space, Final Fantasy XIII and a bunch of others I can't remember. If multiplayer is huge for you, the 360 is the easy choice. More people own them and chances are your friends do to. So if you want to join your friends, it's a no brainer. But the PS3 is the better single player option (which is why I am biased towards it and is why I prefer to Uncharted to Gears of War.)
Anyway, just my 2 cents.