The PS3 has the best games IMO, also, the most diverse library of games.

exc multiplats.
shooters shooters first person shooters third person shooters shooters shooters - xbox 360
shooters action-adventure survival platforming rpg's - ps3

PS3.

If you want to play online, you'll be required to pay for the Xbox Live Gold subscription. With the PS3 you're not required to pay to use any online services other than subscription fees the services themselves might have.

Imo the exclusives on the PS3 are better. The 360 does have some outside of Halo, Gears, and Forza like Shadow Complex, Tales of Vesperia, Lost Odyssey, Left 4 Dead, etc, but nothing compared to the variety you can get on the PS3. Twisted Metal, White Knight Chronicles 2, Yakuza 3/4, Valkyria Chronicles, Demon's Souls, Tales of Graces/Xillia, Heavy Rain, Ico/SotC, Infamous, Uncharted, Little Big Planet, etc..

PS3.

For multi-plats, the 360.
For exclusives, the PS3.

I'd personally suggest the PS3 overall (dat Naughty God), but you can't really go wrong with either.

I mean the PS3 is still receiving games, and the 360 costs money to play online...

Maybe best would be to save some money and get a PS4. PS3 is region free and has much more Japanese games and JRPGs which look also better but 360 is better sported by American companies and American games often look slightly better there.

OP, do you like RPGs? PS3 is still getting RPGs like Tales of Xillia 2 in August 2014, and Persona 5 in 2015.

Why not a PS4 or X1 discussion? I wouldn't quite recommend the older consoles after their successors are out.

i would recommend PS3, just because it has a huge amount of exclusives with a lot of variety on them. for example:

Blazblue CP, Aquapazza (Fighting games)
Valkyria Chronicles, Disgaea, The world God only Knows (SRPG)
Demons Souls (ARPG)
Metal Gear Solid (Stealth)
Uncharted (Action and Adventure)
God of War (Hack n Slash)
The Last of Us (Action/Survival Horror)
Killzone or Resistance (FPS)
Infamous (Superhero Adventure Game)
Gran Turismo (Driving Simulator)
Twisted Metal (Car Battle)
Motor Storm (Arcade Racer)
Rachet and Clank (Platformer)
Drakengard (Hack and Slash with a mix of a JRPG)
The Tales games (Xillia, Graces F, Zestiria,), Nino Kuni, Fairy Fencer, etc (JRPGS)

Plus HD Collections of great PS2 games that you might have missed like Zone of the Enders, MGS, Kingdom Hearts, Jack and Daxter, Ico and Shadow of the Collosus.

and i didn't even got close to naming them all, there is a TON of exclusives for the PS3 with genres that i probably didn't even mention before, also take into account this other things:

- Free online
- PS PLUS (if you decide to get it) gives you good free games every month with discounts on PSN
- a Bluray player.
- and most importantly the PS3 is still being supported by Sony with a bunch of good games incoming, like Persona 5, Kingdom Hearts 2.5 remix, Neptunia V2, Tales of Xillia 2 and Zestiria etc.