.243 for deer.
At one point in my distant youth, I theorized that if I used a varmint bullet in my 6mm Remington, Browning B78, a deer's ribs being not very thick, the bullet would "blow up" when it hit the deers side and spray the vitals, heart, lungs, liver, with little bits of the bullet producing a quick kill. (I hope that sentence was not to complex to have the meaning understood.) The kills were all but instant on the 8 or so deer that I shot over varying distances using a Hornady 87 grain varmint bullet. However upon examination, the bullets had not "blown up" despite being varmint bullets (no channeler). The jacket would peel off and stay in the deer, whereas the core would exit the other side of the deer. In any case, the deer would collapse within 10-20 feet of the shot. Despite the failure of the theory, the 6mm with 87 grain Hornady bullets worked so well, that I did not change the load and it became the only load that I used in that gun for any purpose including deer, crows, et. al.
Aside from my personal observations on the success of the 6mm (slightly more cartridge capacity than .243 win...but its twin none the less), the local respected gun smith (the late Mr. Ron Pederson, father of gun engraver Rex Pederson of Michigan), used the .243 for everything he shot including moose in Canada. He stated that in his experience, there was no need for anything else in the lower 48 if you shoot the critter in the ribs, behind the shoulder. He also stated that there was no reason to shoot any animal beyond 200 yards in sport hunting. He further stated that the idea that larger cartridges give a greater measure of assurance recovering the animal after a marginal hit was just horse feathers inasmuch as if they had been shooting something they could handle (.243) the hit was less likely to be marginal...thus countering the perceived advantage of a larger caliber.
Therefore, he and I agree with the original post that a person with a .243 will shoot better than persons who use larger and bigger stuff.
A side note, my 6mm B-78 had a sharp kick whereas the the .243 Ruger MarkII I have is a real pussycat compared to it. I do not know why...the B78 was(sold it years ago to help finance grad school), heaver.