I'll chime in.
I shoot a .308. Have for many years now.
I give up some speed vs. the 30-06. 30-06 offers a wider range of bullet weights. Also, the 30-06 is a cartridge almost every store no matter how small or rural...will have on the shelf.
So why the .308? I had read a lot about military snipers and was able to access a lot of info for .308 performance in winddrift as well as changing temperatures, elevations, humidity, etc. Is helpful when hunt conditions vary significantly from conditions when sighted in the rifle. My .308 uses a light powder load which kicks noticeably less than a 30-06 which is a plus if needing to get back on target faster.
I only shoot one bullet weight and powder load in the .308 for pronghorn, deer and goat. Knowing how the one bullet performs in the .308 results in high confidence of where a bullet will impact in a variety of conditions when is a bang bang moment on a hunt. I shoot 100 or more .308 rounds prior to each hunt at 100 - 300 yards.
As for elk, I shoot a .338 Win Mag for a little extra range using a much heavier bullet. I shoot the rifle only before elk rifle hunts which is about every 2nd year.
All this said...I think a .270 could have killed every animal I have shot in the past decade, though.