Pretty Great
Let me start this by saying that I am incredibly skeptical of chain campgrounds (for some reason especially KOA's). The KOA Holiday in Durango is great. I was there only a few days before closing for the season and it has snowed in much of the surrounding area so the campground wasn't too crowded. The campground is a little ways outside of historic Durango and less than an hour from Mesa Verde. The tent site I stayed in was near the showers/bathroom and laundry and in the middle of the ground but didn't feel like I was lacking privacy. The cost is basically the same as staying in Mesa Verde's campground and there's paid laundry as well as really great showers in very clean bathrooms. The staff are incredibly friendly. They have gardens on site and, because it was the very end of the season, they were giving away fresh produce for free!