Such problems can be seen in any type of school, public or private. Some public schools are also doing well here and there. If we consider from an overall perspective, in private schools, ordinary children are taken care of very much which is not seen in public schools. Although public schools are doing well in many places but that is not in most places. There are comparatively better things available in private schools. When you send your children to any school, the first thing you should know about that school's environment whether it is private or public.
Let me believe its different in every country. In my country, public schools can have good teachers but the extend to which the student are being cared for is totally different. At the end of the day, whether your kids go to a private school or public, what is more important is the environment the school resides. How safe, supportive, less corruptive, and effective it is for learning. I think that is the first thing every parent should look at for when looking for a place for their kids to school in.