I have hunted mulies and goats my whole life in MT, eastern and western. I have shot them with a 22-250 75gr. and the largest I have used is a 130 gr 270. All have been clean kills. Even the 22-250 put down several mulies for me in my youth. One shot one kill. 165 would work just fine, but I would consider the 150 or less for both. 165 is way to large for goats. It's like shooting a large dog with a cannon. Use what ever your gun shoots best. The goats are going to be your longest shot. The mulies if you are a decent hunter should be 150 or less.

Hyde