With good disposables the AWM lasts about 2-3 weeks, less with rechargables. We're talking heavy use here. It does sleep on its own (and you can turn it off too) so with lighter use you can get significantly more. It comes with a pair of AA disposables. Good silver and blue bunny ones, at least when I got mine.
The AWK takes 4 AAs and can go as long as 2 months with heavy use, much more without.
Benefits:
No wires
Hardships:
This isn't really too much of a hardship, but the batteries change the way the mouse is weighted (compared to the Apple Pro Mouse), this takes a bit to get used to.
The low battery warning goes off way too early.
The AWK has no USB ports.
I'd definitely recommend the AWM. The AWK only if you're really into the "clean" look (which I am, and I like).