Between the Xbox 360 and PS3, I'd have to go with the PS3, and here's why:
The PS3, in my humble opinion, has the best exclusive; I cite Uncharted, Killzone, Metal gear Solid 4, Little Big Planet, God of War Heavy Rain, and Resistance, as my examples. PS3 exclusives also look and run much better than 360 games do. Because a game is only going to be released on the PS3, devs are able to focus on using all of the power of the PS3, like the 8 SPE,(effectively 8-core) CPU of the PS3. Take a look at games like Uncharted 3, and you'll notice nothing on the 360 looks nearly as good.
For Xbox 360 exclusives, the only popular AAA titles i can think of off the top of my head are Gears of War, Halo, Fable, and Splinter Cell Conviction. (There definitely are more, and I'm not implying otherwise, those are just the only really big titles I can think of)
It is certainly true, that with only a few exceptions, like Final Fantasy and Bulletstorm, cross platform games run smoother on the xbox 360. the 360 is a very easy platform to develop games for because of its standard hardware configuration, with a triple core CPU and standard GPU. because of this, developers often focus more on the xbox 360 version of cross-platform games, and then hastily port it over to the PS3, which results in some dull colors, and lower framerates. truth be told, most cross platform games look and run better on the 360 than PS3.
The reason why I still recomend a PS3 over a 360 is because almost all games, including the cross platform ones that aren't great on PS3, you can find on the PC, and they are almost always way better on PC, due to superior hardware. Even a low to mid tier PC is more powerful than both consoles, and nearly everything that 's available for the 360, is available on PC(Halo and gears excluded), and much better.
PS3 also has free online multiplayer, a blu ray player, better build quality, and ALL models have built in wi-fi, whereas only the slim model xbox 360 has built in wifi.
My verdict is this, get a PS3 for exclusives, and a PC for cross platform games.
P.S., it's also only fair for me to note that my Xbox 360 was never connected to the internet, so I have no experience with Xbox live. A lot of people love it, even though you have to pay for it, but I can't have an educated opinion on it.
In conclusion though, you should get whatever is best for you. If you don't have access to, or aren't able to afford and decent PC, the 360 is definitely a viable option to get your gaming fix.