An off placed arrow might kill a bull in 24 hours whereas a bullet in the same location might kill it in 2 minutes. That fact alone means we're likely looking at more lost and dead bulls per hunter in archery than in rifle.
There are no official stats to say objectively one way or the other that i'm aware of. But my mind is made up on the matter.
The real rub, for me, is not who has a greater impact, necessarily, it's that archers have a tendency to be in full blown denial that they have negative impacts on elk herds. They are sooooo ethical and moral, after all