Even though I haven't hunted them yet I'd have to say that the mopuntain goat is the hardest animal by far to hunt. Sheep are hard and do live in similar terrain but you can find sheep a lot lower and in much less rugged country than the goats. Goats are in some of the most rugged and hard to get to terrain you will find anywhere.
I once read an article about thes very question and a few guides commented that most folks usually do not opt for a second mountain goat hunt no matter how successful.