Both my wife and I have killed a pile of big game with the .270, .280 (and me with the .280 AI) and .30-06 over the past several decades. Have yet to be able to tell any difference in "killing power" or practical trajectory between them, as long as the bullet expanded and penetrated sufficiently.

“Montana seems to me to be what a small boy would think Texas is like from hearing Texans.”
John Steinbeck