If you are asking me, they all do the job almost equally well. I dont know much about the 7mm-08, but the 30-06 is king in my family for deer, the .270 is my personal favorite because its a flatter shooter and has less recoil than the rest, and the .300 gives you longer range and a heavier round for big game. And enough recoil to throw my skinny arse around.
I would say the other wildcard would be the .308, a short action cartridge that lets you have a shorter, carbine type firearm that you can handle easily and still shoot at longer ranges.
ETA, see above post. Didnt know that about the 7mm-08. I do know that for me, there is a noticeable difference in recoil between the .270 and 30-06, but for anyone over 90lbs, it shouldnt be much of an issue.
This post was edited on 12/6 at 9:10 am