I've owned several turdy aught six's over my not so many years in various versions; Bolt actions, semi-autos, & pump actions but only hunted with one. Yup an old Remington pump that was handed down from my uncle. It shot a � MOA of a house but did manage to maim & mutilate my first deer in the North woods of Maine at the age of 16. But somewhere a long the way, probably after fulfilling my military contract with the US Marine Corps, I decided I no longer liked cartridges that were/are designed by people to kill other people. If you total up how many people have been killed by the 30-06 & how many animals have been killed with the same cartridge it might be a push these days. So the history of the 06 is something that I prefer not to be associated with unless I decide I'm tired of all the stupid people in the world and it becomes legal to hunt said folks.
Now on the other hand you have a 375 H&H that was design to be used in double rifles & bolt action rifles for killing game animals. Then around 1924 or so the Holland and Holland company neck the 375 cartridge down to .30 caliber & produced the 300 H&H, for hunting/killing game.
To my knowledge at no time was the H&H cartridges designed to kill people, never been put in a machine gun etcetera. It's whole concept was and has been to produce a excellent HUNTING cartridge. And I personally think that Holland & Holland did a fine job in doing so.

If this means I also need to purchase tweed so be it. But my choice is for the 300H&H. It will do everything better than the 06, period.