When I trained on the downhills and ran them hard, there were few problems on race day. The eccentric contractions of the quads on downhills damages the muscle fibers, and can exhaust them of glycogen, leading to quivering muscles. Since we have few big hills in southeastern Wisconsin, I find it useful to do leg extensions in the weight room. The slow drop is not the same thing as what is experienced while running down hill, so I train on our small hills by running them fairly hard. The bottom line is that if I work hard in training, it pays off with less quad weakness on race day, and less quad soreness afterward.
Every race seems to be slightly different.
Since we have few big hills in southeastern Wisconsin, I find it useful to do leg extensions in the weight room. In the back country, one can work the uphill muscles too. George Beinhorn Quads are a tricky deal. You definitely can't prepare for a race with long downhills by running lots of uphills. I've trained very effectively for the downhills, in minimal time, using weights.