I’m betting on the centaur. The hardest part of shooting from horseback is knowing your horse well enough to adjust your shot for its gallop. Try a simple experiment with a camera: go shoot some video while running on a bumpy, broken road. Then shoot the same video from a car while someone else drives. Then go to a nearby major airport and shoot some video out the windows of whatever monorail/peoplemover thing they have.
The rail video is smooth for most people, barring a lurch at accel and decel as it enters and leaves each station. It is like you’re standing still. That lurch is because you can’t exactly compensate for the train movements. Now look at the other two videos.
For most people, there will be less camera shake when running. Your hands learn to compensate for signals from your feet for what your feet are about to do. You learn car movements secondhand from sensing acceleration after motion has started. It’s like the acceleration in the train but continuously adjusted. Horseback is even more variant as the horse crosses terrain.
The centaur knows nir own body. Ne can adjust ahead of time. The Mongol is reading the horse and is always suffering some time penalty, no matter how well trained horse and rider are. So I bet on the centaur.
I double my bet if the Mongol is on a new or untrained horse.