I learned everything I need to know about this debate from Uncle Phil when Ashley started going to public school without telling him and Aunt Viv.
When thinking about the private school ask yourself this question "It's not what I know is there, it's about what I know is not there". If there is something at the public school (bad influences on your kids, shitty teachers) that concerns you, but is not at the private school, go the private school route. If there isn't anything at the public school that concerns you that you could avoid via private schools, go the public school route and spend the extra cash on other areas to improve your kids life, educational or not, but preferably some extracurricular that teaches them discipline.