Not quite correct. With bullets up to 150 grs the .308 and the 06 are ballistically identical. When you get to heavier bullets the .308 lags behind because the heavier bullet is longer and eats into the case powder capacity. But if you stuck any well made 150 gr bullet from a .308 into a grizzly's lungs, you have the makings of a nice rug. Lots of them have ben killed with a .270 too.

But there is no way you're gonna tote a .50 BMG on a hunt. Too heavy and too cumberson.