Thanks to the other poster for linking some studies. My comment draws from discussion with a leading researcher in the area as well as background awareness of research developments, but I don't know studies off the top of my head without doing a search.
The question of pavement vs soft surfaces is AFAIK open from an injury standpoint. Many people would expect that soft surfaces lower injury rates but I don't think we have evidence to support that.
There's also a difference, which may play a role, between short-term knee problems like runner's knee and underlying damage like osteoarthritis.
What follows is just my opinion/interpretation, but might be helpful. Knees in running are a bit like bearings in a car wheel. They don't generally go bad on their own (unless they are overloaded when not ready), but instead because of imbalanced forces around them, like mis-aligned wheels or tire tread wear. The knee has a lot of outside forces acting on it, mainly from the quadriceps and the IT bands, and if these forces aren't in harmony, they will pull on the knee and affect the way it tracks/moves. Since the knee has to move thousands of times over the course of a single run, a small imbalance can add up and cause injury. So a lot of times the fix lies in stretching or strengthening the quads and IT bands (e.g. I find sometimes that a knot in my quads can cause knee problems in running that go away soon once the knot is worked out).