To come up with a decent answer to this question we're looking at the wrong end of the cartridge/game spectrum.
Look at the little critters and shooting them with different guns and you can see more clearly how this works and why.
A chipmunk shot with a pellet gun will often just have a hole through it with even "fast" pellets and caliber doesn't seem to matter between .17, .20 or .22. You get some with a hole through them and some run off.
Start shooting them with .17 or .224 bullets and speed will vaporize them. As you move up through squirrels, chucks, porcupines, raccoons and coyotes, things begin to change. Even a 30-06 with fragile bullets won't reliably vaporize a porcupine or raccoon like a 35 grain VMax will a chipmunk or red squirrel.
What we're really trying to discuss is when does killing power move from reliably adequate to reliable overkill. Relatively fragile bullets in 50 BMG or 20/30 mm would probably be pretty hard on deer of any size, but might be noticeably less hard on moose and bigger. They would likely produce results more inline with small varmints and .224 center fires on smaller things like raccoons and porcupines. I know a 30-06 with even fragile bullets won't vaporize them like a red squirrel.
When you drop below the reliable overkill threshold, then a lot of other factors begin to come into play. There's nothing in NA that I couldn't kill with a .223 and today's tough bullets. Discussions of people having a bad time of it with large dangerous things like polar/brown bears must of necessity be selective for poor/excellent use of the weapons involved.
