I can't comment on really large game; between .61 and .72 caliber on deer, there isn't any difference I've noticed. Both break bone and make fairly large holes, the .72 obviously are notably larger, but don't seem to kill any quicker. Heat treated .510's rate right up there and deer sized critters are butter from one end to the other, if they are employed.
I have seen notable differences in calibers from .355 to .45 caliber on the same animals. In my experience, too small of a hole takes a bit more time before the animal realizes its done. A large enough hole, and the results really aren't that different. Depending on bullet design with solids, for deer sized stuff, that "large enough" is around .40 caliber.
Frontal area rules the handgun/solids world and velocity, noise, racket and recoil is a way distant second to applying that area with a decent SD to vital areas.
One would find an "anemic" 44 Special loaded with a good bullet/design miles ahead of a 180 Buffalo Bore in .357, at least from what I've seen with primarily deer, with shots through the lung/heart area.
On larger animals, I can only speculate that the larger frontal areas perform better, but perhaps not in a linear fashion.
