fwiw, i've been on three sheep hunts - one NV desert bighorn ewe, and two Dall (N. side of Brooks Range). I used a 270 Wby with 140 Accubonds. 547 yds on my desert bighorn ewe. 350 yds on my Dall. (on the other Dall sheep hunt, the guide only left camp twice in 10 days, while i scouted and located sheep on my own, but chose not to risk shooting a potentially sub-legal ram without a guide present as required per regs.) for me, i chose one of my rifles with a flat-shooting caliber, sufficient anchoring power for sheep, manageable wind drift, but light enough recoil that i can easily follow my shots when hunting solo, and not unreasonably heavy to carry. As Mr. McLaughlin above points out, consider whether you'll be in bear country.
fwiw, i would not err towards the light side when choosing a for a sheep hunt, even if not in bear country, because you may potentially be dealing with wind and cross-canyon shots, in rough country, on a potentially once-in-a-lifetime tag or hunt.
fwiw - terminalballisticsstudies may provide some useful caliber-specific info in his "knowledge base" section.