Just my opinions.
Sometimes we loose sight of the bottom line in shooting, especially hunting. The bullet is the only tangible connection we have with game. It is all about bullet choice and placement. A 150 gr Nosler Ballistic tip bullet fired from a 308 or 30-06 into the vitals of deer-sized game will produce the same desired effect, a dead animal.
You can shoot most of the same bullets out of a .308 Win as 30-06. In hunting there is very little difference. The cartidge and rifle are just delivery systems for the bullet.
Something to consider; you can handload your 30-06 rounds to approximate .308 ballistics (less velocity and recoil), but you cannot go the other way. If you need a 180-200 gr bullet for hunting, opt for the 30-06. There are factory 30-06 rounds available that are "reduced loads", which approximate 308 ballistics and have less recoil.
I hunt with both. If I know I will be likely shooting over 250 yards while hunting, I will generally carry my 30-06. But then again my 308 and 30-06 are two different rifles; Both are Ruger M77; The 308 is the International, with 18" barrel. I prefer this in timber and shorter range situations.
My 30-06 is an old tang safety M77 with 22" barrel and has taken game out to ca. 450 yards. This is my no. 1 hunting rifle not becaue of the calibre, but because I know it better than any of my rifles and have the most confidence in it and my ability to shoot it.
If you have to choose for tactical shooting sports, I have no experience in these and offer no opinions.
Again, just my opinions.
Tally ho.
K