Xbox360 may have not as good as graphics compared to the PS3, but I am assuming that is not the only reason you would buy a new system. I believe that the PS3 is only superior to the xbox360 in graphics alone.
If you want a wider selection of games, go with the 360. The PS3 has a very limited library of games you can choose to play from. In addition to regular console games, you can download "arcade" style games from the xbox live market place.
If you want a good online experience for with the 360. Xbox Live allows you to play games online, download other games, movies, t.v. shows, trailers, demos, and if you have a a Netflix account, you can stream videos from the internet to any t.v. your xbox is plugged into. All of these features are available for free except for the playing online games. To play online, you must pay $50.00 a year, or you can pay per three months or month, depending on how you do it. I find this a very small price for what you can do. 50 dollars a year divided by 12 months means that XBL costs about 4 dollars a month. This means that for not even a dollar a week, you get to play games online with your friends. Even if you do not want to play games online and pay, you can talk to people online and download game updates for free.
As for graphics, the PS3 is better in the category, but do you play games based solely on that? If you play the same game on a xbox360 or PS3, is paying more for the PS3 worth it looking a little bit better? The gameplay stays the same. Also, you will not notice that much of a difference unless you have a T.V. that is 1080i.
Also, don't buy the three rings of death scare for the 360's. Unless you buy a used one that was manufactured within the first two years, you are safe. Microsoft fixed the defect, a glue was melting which is now replaced with a nut and bolt, so new machines do not have the faults the old ones have.
I hope that helps