It mostly depends on taste, but the PS3 has a clear advantage.
The advantages 360 has over PS3 are : some prefer the controller, the online service is never online, it's easier to program for so some games run a bit smoother (the only games where there was a real performance difference were Skyrim and the Fallout games.)
-But the most important aspect are the games. And this is where PS3 clearly is the winner.
Xbox 360 is mostly invested in action titles. The PS3 is the only platform on which you can find great games in ALL genres.
The last couple of years 360 has only had Halo (which IMO is one of the most overrated franchises ever), Forza and Gears of War (only franchise PS doesn't have an equal or superior answer to.)
You have to realize this generation of consoles is coming to an end. Sony has revealed the PS4 for a part, probably releasing it by the end of the year, whereas Microsoft is going to show the Nextbox this month. Also probably releasing it by the end of the year.
PlayStation is the only platform that gets good support after its release. Microsoft abandoned the original Xbox when 360 came out, and that system had its last exclusive triple A title early this year. There's only kinect cr*p being planned.
Sony promised a 10 year life cycle for the PS3, there are still several exclusives planned, and more soon to be announced.
XBL (Xbox online service) works better than the playstation network, but PSN is free. For a lower price than XBL you can get PlayStation+ It's 50 bucks for a year, but you can download tons of great free games such as Mass Effect 3, Hitman : Absolution and Bioshock 2. You can also use this feature to automatically update your software and upload your save games to a cloud, if your PS crashes.
However, I own/have owned all 5 PS systems (PSone, PS2, PS3, PSP, PSVita) and none ever broke down. 360 is infamous for lots of broken consoles.
And finally, PS3 has blu-ray, which is great if you own an HD tv. Once you're used to high definition you just can't go back to dvd.