As to the preferred sheep hunt it definitely depends on your goals- Do you want the hunt to be successful? or is the adventure the most important part? Is the trophy itself the most important?
Personally I would say a September Stone sheep may be the best! The most beautiful sheep, longer hair in Sept and great country and the leaves changing. Every sheep has individual coloration. The hunts are usually horseback or backpack. On average the horns are a bit heavier than Dalls. Be careful who you go with, not a slam dunk or guaranteed hunt…
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Second I would go for Dall’s sheep. A full curl Dalls is amazing, a great trophy. The far north and the rugged country they live in to me is the iconic “sheep hunt” it is often the first and only sheep hunt most go on. Historically it was the cheapest and relatively successful option. Unfortunately Dall’s population have plummeted raising prices and killing success rates - especially in Alaska. IMO the best Dall’s hunts are in NWT where numbers are still good and Helicopter access is an absolute game changer- success rates are very high. Very different than my first successful Dall's hunt in AK which was walk-in Solo!
Rocky Mt bighorn has become very expensive and difficult to get a tag. I was lucky to draw a Colorado archery tag and kill one. I like the mountains the Rockies live in better than the country most Cali bighorns are found. Rockies are bigger on average as well. Hunting in the area I lived was nice to scout etc, but wasn’t quite the trip or remoteness the far north sheep provide.
Desert Bighorn- I have not hunted yet, (will soon) I guess I am not drawn to the desert- have been many times and even lived on the northern border of desert sheep (Colorado monument) the spectrum of hunts is wide- easy to super tough. Mexico is a mixed bag but the game ranching (and subsequent releases to the wild to supplement the free range populations) has kept the prices in check. Has also increased the horn size and accessibility to the sheep- depending on where you hunt.