From what I've heard, I think green LED's are less efficient than other colors (including white), so for the same output you would have less runtime (you should research this more, though, to make sure I'm not remembering incorrectly).
As to advantages of green over white just in terms of color, well, I'm not sure. This is something I've wondered about as well, and have done as much searching as I could handle. Basically, unlike blue or red, which have specific areas that they excel (hunting and not disturbing night vision, respectively), I haven't seen a particular use for green.
That said, our eyes are most sensitive to the yellow-green portion of the light spectrum, so chances are, at the same output level as a red or blue or whatever else light, the green will probably appear brighter. I can't say that I know of a really good use for this, but from my own experience, the green lights things up outdoors pretty well.
In the end, though, I think white will be more useful, as it gives you MUCH better color definition than green. Green, however, has a much higher gadget-factor.