As I've said before, you'll see more difference using different bullets within a caliber than between two calibers on deer sized game...
I once saw a deer hit with a .270 in the lungs followed quickly by a .243 through the lungs...The deer still sprinted 60-70 yards before she dropped...
It ain't the size hole it's where you put it...
I've seen and cleaned more than 2,000 deer killed with just about every caliber commonly used from 22-250 through .300 Mag...Plus shotgun slugs, roundballs, maxiballs, arrows, etc...
More deer are lost by poor shot placement and poor tracking than everything else combined...
If I was hungry and had to kill an elk and a .243 was all I had, I'd kill the elk with the .243...More than likely with a lower neck shot or a bullet to the brain...