Take your own likes into it. (In other words decide which you prefer.)
Make sure you have someone you know in real life to play with otherwise you will most likely get bored. You can always make friends on-line though!
Try the systems: Try the Xbox 360 & PS3 thoroughly and see which you like better.
Follow your instincts: if you owned an Xbox and liked it; go with it's next gen counterpart. Vise-versa if you had a PS2 and liked it more go with its counter-part.
See which one has games that appeal to your tastes. (I.E: If you're a huge Metal Gear Solid fan and can't wait for Metal Gear Solid 4, then buy yourself a PS3. If you're huge fan of Halo, get a 360.
TipsMake sure it fits your budget. For instance Xbox 360 is cheaper at only £120( but lacks many features, you should probably go with the next-step up and get the full featured one for £200,) while the PS3's 80GB version is £350.
Consider the systems extra features. PS3-built in Blu-ray capability, Playstation Store, Free Playstation Network, Free online, Chat, Internet, Playstation Home, Xbox 360 has features like in game chat, Xbox Live, and Media Center Extender (For use with Home Theatre PC's).
Listen to your instincts. Your friends may have different opinions so stick with your own.
Pick up a gaming magazine or two (OXM, Gamesmaster, etc) and see what they have to say about each system.
Xbox 360 has a full online community which can be accessed for free, but you have to pay a £25 a year service fee for online game matchmaking. The Playstation 3's online service is all free.
Keep in mind that even though both have standard wireless controllers, the 360 controller has a slightly larger middle area in the back for a removable battery pack (Which accepts rechargeable and standard batteries), versus the PS3 controller without a removable battery pack but you plug it in to the PS3 and charges. Also the PS3 has all wireless controllers. Also consider the drawbacks of each.
Consider a Wii if you dislike either of the two, it has many interesting and innovative features. However, the graphics are not comparable to the 360 & PS3, which support High Definition TV's. (The Wii does not)
Anything you buy can break so take good care of you're stuff.
Remember that graphics and capabilities aren't your first priority, but the games themselves are.