With rare exceptions, there is no private medicine in Russia. "Commercial" clinics can only exist as an addition to the "free" one. That is, you need to deal with a specific case and look for the optimal solution. Relatively speaking, a good dentist can work in any clinic, in the district it just happens less often. Health care is a systemic problem in Russia, the type of clinics has little effect. And for money it is often optimal (cheaper) to receive treatment outside of Russia.
In my opinion, a person who studied with these people at a university, in private medicine, the same doctors as in public (even often worse, but it depends on the level of the clinic), only the equipment is better (and even then not always , again from the clinic level). So it is better to be treated where a good doctor works. For example, my good dentist works in a city dental clinic, and in one unnamed medical center there is a whole brood of non-doctors, the whole point of their work is to issue certificates of medical examination (which is carried out somehow). And my friend's husband works both in a public hospital and in a private one, and there is no difference in his work.
The advantage of a large private medical institution is that you will most likely (not a fact) get everything you need done quickly (and a few unnecessary ones - for your money) analyzes and research quickly and at a convenient time (and not at 8 to 9 on the third Friday of the month), you will be given shoe covers (in my clinic they are chronically absent, and when they appear quickly somewhere disappear) and will be received at exactly the appointed time (because there are many of them and you are alone, and not vice versa, as in the city polyclinic). But for the rest ... The most disgusting doctor I came across was in a paid clinic, where I had to go, because it was urgently needed, and the best one was in an ordinary city dispensary. But in fact, they meet here and there - good doctors and bad doctors.
Take, for example, dentistry. When I was in a private room, there were only two patients in front of me, but they were such that they apparently had no particular problems, so bleach, patch up. Another thing is in the state, where so many people pass, and different: the elderly, oblique, and most importantly with such "sores" that it is immediately clear that doctors in this clinic have much higher experience and practice than private ones. Therefore, I only trust those who have a larger and more varied flow of "material".
From personal experience I can say that paid is better. In the state. clinics even communicate somehow to "fuck off" or something ...
I have been using the services of paid clinics for a long time, the staff is friendly, and the equipment is better, which gives a greater chance of detecting something malignant!)
State enterprises always lose in terms of the quality of services. Anytime, anywhere.
My experience is dental treatment. Actually, I had a chipped tooth, a rather uncomfortable chip, and they told me that the filling would not last long. Three times I went to different free clinics, the filling lasted for about a year, while when the tooth was made, it was not always done carefully and it was painful. I'm tired. I went to a private clinic, gave 2k per tooth (~ 5 years ago in our garbage city it was quite expensive), they did everything carefully, they even picked up the color, the anesthesia was also done painlessly and throughout the treatment, except for the injection, I did not experience any discomfort. The filling is being held to this day.