It also depends on the bullet diameter and bullet weight.
But all else being equal, the answer to your questing (in my opinion and experience) depends on the DISTANCE, the GAME, and the Shooter's LIMITATIONS.
If you shoot a .308 caliber 180 grain bullet with a muzzle velocity at 2,900 FPS at ELK, then your shots should probably be limited to, say, about 200 yards. Given the same bullet, if you want to strech your distance, then the velocity can increase accordingly.
That said, you can kill an elk at 100 yards with a .180 Nosler Partition in a 308 Winchester just as effectively as you can with the same bullet in a .300 Rem. Ultra Mag at about 400 yards.
The thing is that you cannot always predict the distance at which you will shoot the elk. It could be 50 yards, or it could be 400 yards. This is where one's personal shooting skills come into play. If you cannot shoot Elk effectively at distances over 300 yards, then you do not need the extra power and recoil from a .300 Rem Ultra Mag. In this case, a .30-06 Springfield would probably do.
So, all else being equal, the answer depends on the Distance, the Game, and the shooter's limitations.
Zachary