I've done long MTB rides/races on my flat bar XC bike, as well as doing centuries on my drop bar bikes. Assuming the terrain isn't technical MTB terrain, I'd much rather ride with the drop bars. The improved aerodynamics and comfort are the driving factors for me.

As far as flat bars/MTBs go, I have a fairly aero position on XC bike(big saddle to bar drop.) That being said, the bars are nearly twice the width as my most narrow drop bar. In racing scenarios, I'm often holding the bars inboard of the brake levers or holding the aero "puppy paws" position(when on non-technical parts of the course.)

I have carpal-tunnel syndrome in both wrists, my symptoms most often flare up when using flat bars. The multiple hand positions offered by drop bars definitely helps too.