My current dentist is an NHS one working in a small practice, that looks pretty basic/run down from the outside (it has done since he opened up years ago), on the inside though it's pretty good and the actual room where he does the work is just the same as the old one I went to who moved over to private work.
In my (limited) experience, the private ones tend to spend more money on making things look pretty - large, prettily decorated waiting room, nice signage, advertising etc, but aren't actually any better or worse than the NHS dentists when it comes to treatment (if anything the NHS dentist I see now is better than the old one, who now has a a very pretty surgery and is fully private, making a mint out of largely cosmetic work).