http://en.wikipedia.org/wiki/Xbox_360_exclusives#Microsoft_Xbox_360
Heres a list of all PS3, Wii, 360 exclusives (this link goes down to the 360 section). It also shows console if only console exclusive (IE Witcher 2 and Alan Wake)
So if you go 360:
Some decent JRPGS (Blue Dragon, Lost Odyssey, Magna Carta 2, Infinite Undiscovery, Tales of Vesperia was OK)
So-So Open World Mayhem (Crackdown 1, Crackdown 2, Saints Row 1 but SR2 and SR3 were multi)
Very good racing titles (PGR 3,PGR4, Forza 2,3,4)
Shooter Heaven (Gears 2,3. The first was on the PC with extra content. Halo 3,4, Reach etc.)
Shootem Ups to! (Raiden IV, Deathsmiles, Otomedius Excellent)
Couple of unique good ones (Viva Pinata 1+2, Halo Wars, Fable 2 is OK, Dance Central series, various Kinect games such a Steel Battalian)
XBLA Titles: Fez, Shadow Complex, etc.
PS3 definitely has better exclusives, especially if you take out the shooting games.
Edit: Edit for XBLA exclusives and added Tales of Vesperia, Steel Battalian