I have both and I think they're equally as good as each other.
Get a PS3 for their exclusive games (they're amazing) and if you have a good setup at home, (HDTV, surround sound, etc) the added blu-ray player to it is great for movies.
Get a 360 for multi-platform games. PS3 is still fine for that too, but there's usually more bugs on the PS3's version and DLC for games nearly always comes out first on 360. I also prefer the 360's controller, although personal preference.
I enjoy playing both online, although live is a bit better. Xbox Live is $50+ a year and PSN is free. The benefits I get on Live compared to PSN is party chat and a cleaner, more user-friendly interface. PSN is still very good though for a free online service.