Flat bars have basically one hand position, with the wrists fully pronated. Drop bars have at least 6 different hand positions, most of which allow a more neutral wrist position. Also, in most of those positions the arms run straight from the shoulders to the bar, rather than splayed out to the sides. If you're riding into the wind, or down a descent, you can get in the drops for better aerodynamics.

The key is that the bike has to be set up properly. It's not like you put a drop bar at the same height and distance as a flat bar, because then the hoods will be too far away and you'll end up riding on the tops all the time.