Okay, I've got an iMac, a very decent PC, a Wii, an X360 and a PS3.
My advice?
Buy a PS2, seriously, that "2" is not a typo. The console is cheap, the games are cheap and the line-up is just amazing. You'll find a handful of must-play games no matter what genre you're looking for (except MMO and RTS, obviously).
But, since that's not the answer you're looking for, let me give you the rundown:
X360:
If you like shooting stuff. And racing, I suppose. Personally, I think the console is bleeding. Badly. Back in the day, it had all the big games and exclusives: Lost Odyssey, Mass Effect, Gears of War, Halo, Eternal Sonata, Blue Dragon, Infinite Undiscovery, etc. Sadly (or thankfully) quite a few "once exclusives" have gone multi-platform (Eternal Sonata, BioShock, Mass Effect, Star Ocean 4), and most newly released games are multi-platform anyway. So there's not a lot of incentive left. Also, Mistwalker hasn't released a decent game for the X360 in years, Rare is doing Kinect games and Bungie... Was is Bungie doning these days?
Also, remember, controllers don't come with built-in lithium batteries, so you'll have to buy a sack of AA-batteries. Or shovel over some extra dough for a charger pack. Oh, and if you're planning to upgrade your HDD, be warned. It doesn't just take any type of HDD, you have to buy special ones that cost at least three times more than a normal HDD.
PS3:
Just throwing it out there, their online service got hacked and they didn't handle it well. I don't use my credit card, so no worries for me, but it's not because it doesn't affect me that it isn't a serious flaw worth mentioning. But, besides that, it has a blu-ray driver and a pretty decent game library, with games such as: LittleBigPlanet, Uncharted, Resistance, Ratchet & Clank, God Of War and InFamous.
Fun facts: you don't pay to play online, controllers come with built-in lithium batteries and you can replace the HDD with any other 2.5-inch SATA notebook hard disk. I myself shoved half a gig right in there. Quite nice.
And sometimes necessary as well. Where the X360 will often give you the option to install some game data to make the game run faster, on the PS3, it's often mandatory. So yeah, that can be an annoyance when you buy a new game and want to get right into the action.
Conclusion:
Just look at the game library and decide for yourself, Halo or Killzone, Resistance or Gears of War. Viva Pinata or LittleBigPlanet. InFamous or Lost Odyssey... wow, that last one wasn't even close to making sense. Personally though, I have gotten much more out of my PS3 than my X360 (especially after my first one red ringed on me, devilish bastard).