Depends on the country, the particular system, and which parts of the system you're talking about.
In Australia, the best surgeons are generally the ones with jobs in both the public sector and the private sector. In fact, there's more cache/prestige in receiving a public sector appointment than there is in running a wholly private practice. The view (generally) is that those that are in private practice couldn't hack it in the public system and had to move to the private sector because they couldn't measure up to the standards.
Even within Australia though, that's variable. There's a move favourable view of private sector only surgeons in Western Australia and Queensland than there is in NSW or Victoria, for instance.
The difference between private and public medical practice in Australia comes not in the standard of medical care, but in the standards of things surrounding your medical care. So, in the pay-for-play sector, you get nicer rooms, better beds, better food, better rehab, more follow-ups, better attention from nurses, ect, ect.
However, on an actual medical basis, there's no difference in the standard of care and the medical outcomes (in Australia there's a very slight bias in most medical disciplines towards better outcomes in the public sector).