RE: .308 or 30-06
Ballistically they are pretty close. Doubt that the critter would know the difference with few exceptions. It could be hard finding a lever action 30 06. I think the 308 is inherently more accurate, but that is not to put down the 06. Both were used as sniper rifles. The 30 06 can load up a bit heavier bullet. Ammo for both is very easy to find.