In a perfect world I would brake in both places as its easier on the car, but the simple fact is that you can't drive a considerable distance down the mountains (at least not the ones where I live) without overheating the brakes. Brakes that are way overheated are not good. I would much rather stress my engine against gravity than have mushy brakes coming down a steep incline at 60mph.
Although downshifting would be easier on a flat surface, its also not necessary. You aren't going to overheat your brakes on the street (at least you shouldnt if you drive normal).
But dont take my word for it, just ask any trucker or any other CO native. Downshift when you are coming down a long hill.