I own both and use them both for media playback. Personally I prefer the 360 because of the better GUI. The short of it is that it depends on what kinds of media you'll be playing the most.
If it's primarily BD and DVDs, go for the PS3 since the 360's DVD controls are horrid and BD is nonexistent.
If it's AVI, DIVX or some other compressed format, I'd get the 360. The 360 plays almost everything I've ever thrown at it, while the PS3 pops up a "corrupted data" screen on some DIVX files that the 360 will play. I don't think I've run across any situations where the opposite was true.
If you're looking for a Media Center Extender, it's 360 all the way. While the PS3 can play MS-DVR files (much to my surprise when I found that out), it doesn't do so very well resulting in a choppy mess from what I've observed on a wired connection with everything set up correctly.
Extras: PlayOn works equally well on both and from what I've read the 360's Netflix integration is better (although I haven't actually used the PS3's version).
EDIT: Forgot about music playback. If you're concerned about visuals and GUI, the PS3 wins hands down. The 360's music player is just pathetic and hasn't been improved since launch (only reskinned).