I haven't really played a PS3 so I can't really talk about that, but I have a 360 so I'll tell you about that instead. And no, I'm not a fanboy.
Xbox 360 - Good
There is a really wide variety of games already out
The online gaming works very well
It has TDU of course
It's really easy to use if you have half a brain
It's easy to set up media streaming for you music, videos, pictures and radio
If you get Live you'll get to play with most of the lovely people on here (me being a lovely person of course :D:p)
There is a lot of DLC readily available
You can get Race Pro next month for the 360
There is a party system so you don't have to talk to the "squeaky" people if you don't want to
The pad fits perfectly into your hand, or it should do
You can buy films off the marketplace and also rip music to your HDD
Some Xbox's don't die no matter what
It's cheaper than the PS3
You can use Messenger whilst playing games
You are allowed to use USB keyboards
You get the ability to mute or block communication with people online
Xbox 360 - Bad
Microsoft don't allow you to use none-certified products with the Xbox, such as steering wheels etc.
Some consoles can be very loud
Some Xbox's are prone to crashing and RRoD
You get some very immature people online, like all online gaming
Some of the DLC is a bit pricey
If you have a bad broadband, you will always get lag
Some consoles are very loud (mine sounds like a plane taking off)
That's all I can of for now and if I think of anymore I will add them. Hope it helps.