For the average shooter. None at all. One has a larger gamut than the other, and some folks will SWEAR by one over the other, but it really doesn't matter for a great majority of those shooting out there.
I thought though that sRGB was the only one that was well supported over the internet whilast Adobe RGB is far less supported (and thus shots can look desturated and dull when saved in that colour space and put on the net)
Unless your final destination (print shop, etc) wants AdobeRGB, you're safer staying with sRBG. Most corner stores will use sRBG, it's widely supported by browsers if you're posting on the internet.
If you want your shots to look good (or at least what you think they'll look like) contact your printer before you get your images ready. They'll advise you color space, DPI, etc. The closer you match to them, the less work you let a computer do.
Personally, about 80% of my stuff goes to the web, and 20% goes to print. I use MPIX for everything exept book publishing (which almost always required CMYK, the bastards). MPIX uses sRBG so that's what I use.