They each have their pros and cons.
Xbox 360 is preferable if you're looking for multiplayer games and if you're interested in a lot of first person shooters. The Xbox's notable exclusive games are things like Halo, Gears of War, and Left 4 Dead. The online multiplayer service requires paying for a subscription.
PS3 is better for people who prefer single player or action/adventure/RPG kind of games. They have some really excellent exclusives, like the Uncharted series, Heavy Rain, and the God of War series. Having a built-in blu ray player can be a notable plus. The online multiplayer service is free.
If you're interested in getting into motion-controlled gaming at all, the 360's Kinect system is far superior to both the Wii and PS3 Move.
The Xbox system is usually a little cheaper than the PS3, if that matters. There's usually about a $100 difference at most, and it can vary depending on the size of the hard drive you want (or any other additional included features).
If you're unsure about what size of hard drive you want, it may be helpful to know what it's used for. Not only is the console's hard drive used for storing game save files and other information, but it also will hold any games, music, movies, pictures, etc. that you want to download to your system. If you plan to store a lot of movies and things like that on your system, you'll definitely want more storage. If you only want to use your system to play games, a smaller amount of storage space would probably be fine.
I have a PS3 myself, and I love it. I've also briefly used both the Wii and 360, and from what I know about them, they're both good systems as well. It just depends on what you want as a gamer.