It depends on the public schools, even in our country, there are some public schools that are far better than some private schools. There are some private schools especially at the secondary level, that relies solely on corp members. It is only well established private schools with good connections that have the capability to supercede public schools.
You don't find many public schools better than private schools. Not saying all private schools are better but public schools are mostly nothing to write home about. The structures, teachers not showing up or doing that at their will, skipping classes and the like, because no one is really holding them accountable and more. Some private schools are not there as well, but most public schools don't do better; lower levels of education particularly.