Comment by carlob
Usually the medical part of it all is strictly worse in the private sector (at least in my country) because the public system has a pretty strict competitive exam to get in, whereas profit driven private companies hire the cheapest doctor they can get.
Not everybody realizes that and they often fall for the single room in the hospital.
Shorter waiting times is definitely a thing though, especially for non life threatening conditions.
In the UK a large proportion of the doctors are the same. Sometimes even using NHS operating theatres, or with NHS trusts running the clinics, as they are allowed to run for profit services to supplement their budgets...