Depends on the cartridge entirely.
Not exactly. It's not the cartridge, it's the speed of the bullet. And while the cartridge does play a huge part in reaching a given speed, it is the speed (velocity) of the bullet and the bullet's construction (in all factors) that determine terminal performance.
Cup and core and non bonded plastic tipped bullets seem to do better with impact speeds under 2900fps or so.
Not disputing your observation, but I will add that it only applies in some situations. "Do better" at what? On what??
Controlled expansion and adequate penetration on big game? It's what a lot of people think of, but that's not what the OP asked. The OP is vague, asking only about "hunting" and not a specific type of hunting, and there is hunting that isn't big game hunting.
I've had completely successful bullet performance with cup and core bullets at impact speeds in the 3600-3800fs range. The bullets did exactly what they were built to do, expand instantly and completely fragmenting in an explosive manner.
While that's not desirable performance when shooting deer, it is exactly the perfect performance for shooting woodchucks.
Every bullet made to expand is made to expand a certain amount in a given range of velocity. Slower than design speed, expansion is less than design intent (down to no expansion at all if its too far below intended speed) and faster than designed speed does the opposite, resulting in overexpansion which MAY result in bullet "failure" for a specific task.
You have to match bullet construction (design) with velocity, and performance for a specific task.
Bullets designed for moderate or low speed performance can be seriously overdriven at higher speeds, resulting in "failure" to stay together.
Examples abound, one common one is some light (125gr) pistol JHPs optimized to expand well at pistol speeds, over expanding hugely when driven several hundred FPS faster from a carbine barrel.
You can get a similar result from shooting a .30-30 bullet at .300 Win Mag speed.
Another is driving a .45-70 bullet designed to expand at 1300fps at 1800fps. (or faster!
) at those speeds they work more like varmint bullets than controlled expansion big game bullets.
Its up to the shooter to match the right bullet, at the right speed to obtain the "right" performance for each different shooting situation. Not doing that properly isn't the fault of the bullet.