I own both but I haven't played my Xbox in about 2 years for reasons that will take too long to explain. A big advantage the PS3 has over the Xbox is that it's games are region free. That means that you can buy a PS3 game ANYWHERE in the world and it will work on your PS3 regardless of where you bought it. Xbox is still limited to NTSC/PAL. Graphics are the same although I've noticed that the PS3 has more games that have better graphics such as Heavy Rain, God of War III, Metal Gear Solid. Xbox has a quicker connection but then again you are paying for the service, PS3 online play is free. The Xbox marketplace seems to be filled with more stuff and tons of fun games too while the PS3 doesn't have that many things in the marketplace compared to the Xbox.
A very cool feature the PS3 has is "Playstation Home",
here is a video that gives an in depth explanation about what it is.
Xbox360 has gamerpoints with which you can show off to your friends, there are lots of achievements to complete compared to the PS3 which gives Xbox360 games a high replay value in my opinion. The PS3 just has a basic trophy system consisting of Bronze, Silver, Gold, and Platinum. Instead of Gamerpoints you get levels, I'm at level 5 but I rarely see people higher than that level and I don't really go for trophies either.
That's all I have to say, I hope this has helped you out!