Drops, on my MTB. I don't know why I bother calling it an MTB, it has one gear, I keep my eye out for a cheap crank that has a bigger chainring, and the tires are 1.25" slicks inside fenders that look too big, but it did start life as an MTB. I have also raced on dirt with clip-on aero bars on my XC bike (many-hour race with paved portions and technical dirt portions and seven miles riding up a river), so I clearly have lost all sense of what is "correct".

It took me a while to get here, though. I started commuting on flats with long bar ends (on the same frame), and would have told you I valued the upright position, yada-yada. But, in the interim, I became a semi-converted roadie, and started putting way more miles on the road on a 700c drop-bar racing bike than I did on dirt. Now, I value the multiple hand positions and the ability to be in an aero position when desired. I estimate I spend 75% of the time on the hoods, 15-20% in the drops, and the remainder on the flats (or 'Look, Ma'-ing).

Is it "correct"? I don't care. It is comfortable, so I do it. I suggest you do the same.