RE: Alaska Dall Sheep
Generally earlier is better from what I've heard with sheep hunting mainly due to the weather. Lots of folks get out right on the August 10th opener, but ocassionally they still get caught in bad weather. I'd opt for August if given those couple of options, but that is because moose season kicks into gear usually on the 1st of Sept.
I take it you are going guided or with family? What did they suggest?