You have raised a great question. I too, have a child and have chosen to send him to a private school. There are some public schools who test higher than many private schools. Here is what I have experienced with the private schools to date.
There is a noticable difference in the faculty, and parental involvemnet in my particular private school. The school is teaching the kids about respect for the fellow man, as well as the importance of a hard work ethic and dedication.
I can't say the same for many of the public schools in my area. My wife is a teacher and the largest difference and the reason we chose to spend 4500 a year for a 6th grader is in our public schools there is a sever lack of parental guidence which in turn leads to troubled children.
But, this is part of our countries issue not just my area. Flint, Mi. second only to Detroit as the worst public schools in the country though.