939 is "old technology," it uses DDR memory instead of AM2's DDR2. AM2 uses 940 pins, but it is a different pinout than the Opteron (and old-school FX) socket 940, that's why it's called AM2 instead of keeping it at socket 940.
Right now, either platform will work just fine, you really don't need (meaning probably won't notice) the added bandwidth of DDR2, though if you're thinking of the future and Vista and all that, you may want to go with AM2 since Vista is going to be such a hardware beast.
Anyway, because of DDR2's lower voltages it'll suck less power and should run cooler, but again, I really doubt you'll notice the difference.
Both 939 and AM2 can use dual-channel memory by the way, it's socket 754 that is limited to single-channel DDR.