Im not 100% sure on the detailed differences, but thre are some subtle differences in the riser length I believe, as well as the limbs. The MOAB has a bit more R/D to it.
I have 2 MOABs and a III. Both bows shoot awesome, I have a hard time comparing as the III I have is only 41#, and my MOABs are 52 and 57.
I know the III, with the lghter weight is a nail driver, and I shoot that one amazingly tight.
Not to take away from the MOABs, I have those 2 and just ordered another one. It is dead quiet, and NO handshock. They both shoot right where you're lookin, and I wouldnt own any other longbow other than a Thunderstick.