The .270 vs .30-06 debate has been going on in hunting camps and hunters circles since Winchester introduced their .270 cartridge back in 1925. I doubt that it will be ended here. I also doubt that any animal properly hit with a bullet from either cartridge would know the difference.
My first centerfire rifle was a .30-06 that I successfully used on many deer and elk hunts. I now also have a 270 Win. I have friends that have killed dozens of elk with their .270s. One of them had his American buffalo hunt filmed for the TV show "Hunting the High Country" and he made a one shot DRT kill on a large, old bull with his .270 Win.
With the proper bullet and bullet placement, either cartridge can be successfully used for just about any North American game animals.