Clearer textures, better colors, and a much longer view distance—the PlayStation 3 version of Skyrim has it all. That's not to say that the Xbox 360 version is ugly in any way, only that it doesn't look as good—or as clear—as the version on the PlayStation 3. Additionally, the Playstation 3 version of the game appears to have higher detailed shadows—ones that don't bounce around when the player moves the camera.
There appears to be very little to no pop-in on the PS3 version of the game—a detail hugely noticeable on the Xbox 360.
Spellcasting, combat, and framerate look about the same, with little to no difference in quality.
German Youtube channel AllGamesAlpha have posted up a side-by-side comparison of both the Xbox 360 and PlayStation 3 versions of Skyrim, which shows off just how the game looks on each platform. Just watch it for yourself.