Privacy and natural surroundings are our biggest criteria, so as a rule we avoid private campgrounds. As you all know, being sandwiched between larger RVs can be annoying. Yet we've stayed in State and Federal Parks where, due to the layout, we had no privacy, little in the way of natural surroundings, and were situated between monster RVs. We'd go for a walk and could hardly find our Burro! Generally DNR or other less devloped campgrounds suit our purposes, but as many have stated, when in route compromises are made.
Having said that, we had to stay in Great Falls MO in 98 to receive an award for my ailing Dad from the Lewis & Clark Trail Hertiage Foundation. We stayed in a small, lovely, quiet, treed private campground just out of town. Not much visual privacy, but felt private and serene, a green oasis to return to each HOT day we were in GF. So some private campground owners know how to do it right.