Flags and Nomercy448, in a way you are both right. Flags is by saying dead is dead. Overkill is pretty much impossible. Nomercy448 is correct in saying there are many more efficient cartridges out there that have plenty of terminal performance for whitetail. Now, where the sticky comes into play is if one reloads or not. And not only because of performance pluses that come from reloading but also being able to match up a good performing bullet to a case that the factory loads just don't put out there or they do so at an expensive cost. For whitetail, neither the .270 nor the .30-06 are needed at ranges that most hunters should not be going past. Neither is my .300wm but that doesn't make it wrong to use it.
As to the OP's question, it is a question that has been bantered around deer camps for many many years. And it will probably continue to be a heated topic among hunters for years to come. If one is limited to factory rounds then for the continental US big game species I would have to give the nod to the .30-06. While the .270 can and has dropped many elk and moose, I tend to lean toward the heavier bullet selections that the .30-06 has available in both factory selections as well as reloading.