I alternate between a set of bullhorns and a set of drops (currently riding with a set of Cinelli road drops, bare of course ).

I find that, when riding the drop bars, I spend lots of my slower cruising time with my hands on the flats, right up close to the stem. I use the drops when I want to sprint or climb, when I want to hustle or take off quickly, when skidding/skipping, and when it's windy. I find that getting low helps me put a little more power into my stroke.

When riding with the bullhorns, I tend to ride with my hands on the horns more than the flats. This makes me think that it's more about hand/arm position than height; I seem to be more comfortable going balls-out when my hands are gripping something parallel to the bike frame, not perpendicular (as in risers, flat bars, etc.).