A lot of guys on here have been out west.
In my experience I would not take anything less than a 3o0 Win mag. I currently shoot a light weight 338 lapua... I have taken multiple Elk, multiple Mulies, multiple Caribou, and a Grizz. Not one of those hunts would I have been happy carrying a .308 (who carries a .308 in Grizz country any way???)
My Grizz was taken with 4 shots of 300 win mag (220 partitions)
Most of my Elk were taken with 180 grain partitions or 225 grain accubond (2 shots in ever single one of them)
The mulies same as above
.308 is a great rifle for east of the Mississippi whitetail, once you go west and have wind, elevations, the margin of error is greater.