I should clarify I suppose, my bear tolerance could be higher than others possibly. (Or rather, probably.) I can’t think of a sheep hunt in the last 5 or 6 years where we didn’t bump a grizzly in the timber at sub 50 yards, and there has been exactly zero shots fired.
Carry whatever lets you sleep at night, but don’t focus on the wrong variable if you are worried about close range bear encounters. Most people are real unlikely to carry a big enough bear gun where bore size would actually make a difference on a sheep hunt.