Does it matter?
With the question you originally posted, I can't believe that the choice of caliber would mean anything at all. All 3 are ample for whitetail. I've use the '06, but I have a few friends who have 7 mags and 270s. All of them have produced "instant" kills, and all have required a tracking job, even with double lung shots. Placement and bullet choice would mean more than caliber. I have killed deer that did not take a step, one that was on a dead run and leaping impressively over blowdowns that pretty much died in mid air. At other times, friends and I have solidly hit deer with good double lung shots, and the deer have run over 100 yards. If a bullet expands pretty quickly to do enough damage, and exits to leave a good blood trail, what else can it do?