Another point is that in pubic schools classes range from 20-50 kids, when in private schools the graduating class usually consists of about 50 student. When there are less students in a class, the more predictive the class is, and the more work is being understood and done, and if any student needs help, they are able to get it and work towards their goal a lot better then in any public school that focuses their attention on groups rather then individual students.
Since the students parents have to pay for private schooling the child is usually reminded everyday that they are paying extra for their education and that they have to work hard if they want it to stay that way.
But the major downside to private schooling is that it is not very common to have many private schools in one area, they are usually located in areas where the parents are willing to pay extra for their child's education.
These are some reasons why I think private schools are better then public schools.