Compared to the coastal regions of the country, the Plains were thinly populated. Hunting, especially for buffalo, was the mainstay of the Pawnee and Sioux, and the large range of that animal forced the tribes to be nomadic to some degree, and limited their overall numbers.
So I would say there are three major reasons why the Sioux were the most powerful tribe on the Plains in 1860. First, the region would not support other competitor tribes and three Sioux had come to mostly dominate over the years. Second, the trade in guns and ammunition had reached the Montana territories, so the tribe was better armed than most had been when contact with whites took place, and third, Montana and the Dakotas were some of the last regions in the Plains to be settled and ultimately conquered, so you could say the Sioux were one of the few tribes still largely intact and unaffected by either war or disease.