I helped a friend pack out a bull on MT’s 2019 opener that was killed with a 308. 165 GameKing went in ahead if the shoulder, got into the lungs and a bump under the skin behind the opposite shoulder.
308 is gonna be shorter and lighter and easier to carry, in some rifles very lightweight. Sure the 300 will have more go, but unless you are laying on your nutz with a dead solid rest, you wouldnt wanna be shooting the 300 any further than the 308. I am not downing the 300, have killed elk with one and its a great getter.