I don't own a xbox360 or ps3, but if I would buy one I would go for the ps3. The ps3 has more exclusive games that I think look awesome (especially uncharted) and the online network is free. The only xbox360 title that I would like to try is Kameo Elements of Power, but that game alone is not enough to purchase a console. The current focus of microsoft on kinect is not very promising for the future exclusive xbox games, although all the HD remaking of Sony is also something that shouldn't be encouraged too much. I stick to the ps2 and wii though, because there are still so many awesome action/adventure games for the ps2 that I haven't played yet and the wii has more 'Smitie friendly' games (so no FPS with way too smart enemies...I want zelda-like games ).
You really can't go wrong with either one. The consoles are so similar it really depends on personal preference.
I've always stuck with Sony through Playstation 1 and Playstation 2, but for this generation I have to say that I personally like the Xbox 360 a bit better. I'm a big fan of online gaming, and that's where Xbox 360 is best. Sure PS3 has free online, but in my opinion Xbox Live is worth every penny. I also like the 360 controller. It's as perfect as you can get with a game controller.
Playstation 3 does have better exclusives though. I've never been a Halo fan for some reason, and I can't really think of a 360 exclusive that's a must-have. And I admit I did get the dreaded Red Ring of Death on my 360 last year, after 3 years of running perfectly. But Microsoft fixed it for free, their support is pretty good when it comes to the RROD.
I do want to get a PS3 eventually. I've been dying to play games like Metal Gear Solid 4, and Uncharted. But the industry is moving towards fewer exclusive titles, with titles like Final Fantasy now available for both consoles.