The traditional drop bar is a maes bend, not today's brifter-centric anotomical bends and shallow drops. You can note the difference in Randy's Marinoni shots and the vintage bike bar shot.
The bull horns are similar in height to newer brifter-centric drop bars where the tops stay more horizontal. If you don't ride on the drops, a bull horn bar is an alternative for vintage bikes with maes bend bars. Note the positions of your wrists with each bar and lever config. Bull horns place your wrists at a more ergonomic position and the brake levers are at optimum leverage. Brifters (and traditional levers) are a compromise of leverage when brakes are operated from hoods. The lever and its placement must accommodate more than one grip position.
It's good to have alternatives and thinking outside of the box. Bull horns are not just for time trials, and posing on hipster hardware.
+1 I have ridden road bikes with bullhorns and have noticed a couple of difference. First, the horn portion of the bullhorn is generally longer and usually flatter than the portion of the drops from the first angle to the brakes. As a result, the bullhorns provide more comfortable and different grips in this area. Second, because you do not have to allow for the drops, you can set bullhorns at an optimum height.