Realistically, the .308 is under gunned for brown bears, and that's about it.
If the .308 is under gunned then so is the 30-06. They are that close to one another in performance.
My question is, what can the 06 be used for that the 308 can't?
Nothing.
The .308 only gives up about 40 - 50 yards to the 30-06 in terms of down range energy at any practical hunting distance and the average hunter.
The .308 only gives up about 1.5 inches in trajectory at 400 yards if both are zeroed at 200 yards.
In other words.... same same.
so again what is the 308 to small for?
IMO, only large dangerous animals like brown bears, etc...