I have taken all four North American sheep and none required heavy medicine. The only bear encounters I had during my five different sheep hunts were in Stone sheep country and my guides always carried rifles suited for close up bear possibilities. I never felt threatened.
To me big bore calibers are overkill for sheep hunting for several reasons:
1. A big gun might be useful to fend off a bear but that is one of the main reasons you are required to have a guide. He takes care of bears and you are there to kill a sheep. (If you are a resident without a guide then that may be a different story, but studies indicate bear spray is more effective at keeping you safe than a gun anyway)
2. Sheep are not big boned animals and if a good bullet of any reasonable caliber (6mm up) is placed in the vitals they die quickly.
3. For the majority of us, we are more accurate with smaller caliber rifles with less recoil.
4. Sheep live in nasty places and big guns generally mean more weight. If your rifle weight keeps you from getting into good sheep country, or wears you down before the hunt is finished the big gun has ruined your hunt.
If you can get a large caliber rifle under 8 lbs., which for me is maximum sheep hunting weight, and shoot it accurately, then what I said doesn't apply to you.
For what it's worth, I toted a 6.5 man bun on my final stone sheep hunt and did it with confidence. And that's my take.