A 30.06 is suitable for any hunting in Alaska.

To my way of thinking, it's more about the optics than the caliber. A .375 with a 3x9 scope is next to useless in a bear encounter since such events happen so suddenly and at such close range that a mid-powered variable leaves you blind when you most need it.

I like my .350 because it gives me some extra penetration, but really it's more about the compact size and the optics. It's quick to get on target at close range, but still has the range to whack a deer or caribou out to 250 or 300 yards.

A shot to the center of the face will stop a bear every time, assuming your choice of bullet is appropriate. A shoulder/chest/torso shot might stop a bear or it might not.

I pulled the frame below from a video of a bear attack (not taken by me). This is what it looks like, though in this case the water is slowing the animal down to 15 or 20 miles per hour instead of 35 to 40 miles per hour. You have one to two seconds to swing your rifle up and put the bead on the bears nose. God help you if you're sighted in 3" high...