All the comments about the .308 and .30-06 ballistics are correct, but there are lots of assumptions being made.
They would be accurate as long as both rifles like the same weight bullets.
I have a .308 that shoots 150 to 168 grain bullets under 0.6 inches at 100 yards. It shoots 175 grain bullets OK but not as accurately and I have to forget about 180s.
The .30-06 shoots 180s, 200s and 220 grain bullets very accurately and can barely shoot 150s and 168s under 0.9 inches.
In my case, they really aren't interchangeable.
Of course, you won't know what any barrel will really like until you shoot some ammo through it, so I would hesitate to conclude that even any two .308s will shoot the same ammo equally accurately.
Unfortunately, that means that if you happen to buy a .308 or .30-06 that only shoots light bullets well, you may not have the elk rifle that you were hopeing for.