You'd have to break it down by specific hunts/units/states.
Among the toughest to draw sheep hunts would be a 680 MT Breaks ram tag for a NR, with odds of about 1:2200 this year. At the same time there are bighorn tags in Colorado with draw odds of better than 1:30.
There are Utah Mt Goat tags with extremely low odds, but at the same time Idaho's Mt Goat tags run about 1:40 odds for NR's.
You can pull some limited Elk tags in Colorado with 100% odds. At the same time, a Utah San Juan Bull Elk tag in the random draw this year had odds of 1:1700 for NR's. Interestingly, your odds to draw a NR Desert Bighorn tag in Colorado were 1:387, meaning roughly 5 times better odds than drawing the San Juan bull tag.
So the only point is, you can't really characterize "tough to draw" by just naming the species. But if I had to pick just one species to stand alone as the toughest tag to draw period, it would probably be a Desert Bighorn Ram. At the same time, you could pick up the phone tomorrow and book a hunt in Mexico.