Part of being an ethical hunter is not to take low probability shots. You don't have to be off very much with a head shot to horribly wound the animal, that will then be able to run away unencumbered by the wound, and travel for some distance, never to be seen again. Therefore most hunters opt for s shoulder or lung shot, as these provide the largest target on an animal that might move at any moment. Typically game is shot from an estimated range where it is difficult to keep the bullet strike within several inches of the intended point of impact, rendering the head shot unreasonable except in special circumstances.
So we must first understand what the bullet does that kills the animal. The bullet first and foremost be able to penetrate deeply enough to damage the organs which sustain life by providing oxygenated blood to the brain. If the lungs, heart, liver, or major arteries are damaged, the animal dies a quick painless death. The speed by which the animal dies is determined by how quickly the blood supply is depleted. A big hole bleeds more freely than a small one. Thus a bullet with a large frontal area directly impacts more tissue than a bullet with a smaller frontal area does, so all things being equal the animal dies more quickly. Therefore we choose expanding bullets which dramatically increase in frontal area, damage more tissue as they pass through the animal, and ensured straight line penetration by moving the center of gravity to the front of the bullet. But the problem here is that as the bullet's frontal area increases, its penetration is decreased, so increasing weight is the surest way to ensure penetration. Increasing velocity creates faster and more explosive expansion which reduces penetration even more. Thus I prefer heavy for caliber, large caliber bullets, fired at a moderate velocity for big game. There are other points of view.