Alaskabushman and Paul B, nobody has said the .30-06 was not accurate nor it or the .308 could not take game decently.
And all those deer were killed with bullets, not cartridges. The rifles just shoot the bullets and have no idea where they went. There's no way game animals know what gun held the cartridge that shot the bullet they get smacked with.
Four identical 30 caliber bullets moving at 1642 fps striking game the same way will all perform equally. Even though they came from four different size cartridges such as the .30-40 Krag, .308 Win., .30-06 and .300 RUM.