As it's been explained to me. The two main advantages to a drop away are that the effects of bow torque are reduced and the fletching contact is totally eliminated.

With a prong style rest, if you torque the bow handle, the bow will tend to jump to one side or the other upon firing depending on which way the torque is applied. If the back end of the arrow has just left the string and is still in contact with the prongs, the sideways movement of the bow and thus the prongs, will push the back end of the arrow one way or the other causing an errant shot. Since the drop aways are no longer in contact with the arrow after it leaves the string, the effects of the bow torque are reduced. There will still be some error because of bad form, but it will be lessened.

The fact that you can put a really hard helical on the arrows while using a drop away means that the arrow will stabilize more quickly, so even on a shot with bad form, you will hit closer to the mark than if you're using a prong style rest. Helical fletchings are not necessary, but there should be no argument that they are more forgiving. I have always shot straight feathers because it was such a pain to tune helical fletching with a prong style rest. Now that fletching contact has been eliminated, I will be using helical fletchings with a drop away from now on.

They are not the cure-all for all archery problems, but I do think they are an improvement in rest design.