I had a wonderful public school experience, my husband had a horrible private school experience. I've heard a lot of stories from both sides of the issue, partly because this is a favorite debate of mine.
I think that it depends on quite a few things- your income, your area, the quality of your public schools, the quality of the private school you're considering, and your child's needs.
I think that for the vast majority of private schools as compared to the vast majority of public schools, on most peoples' income, public schools will give you more bang for your buck.
Most of the private schools in my region (I'm a Georgia expatriate living in Texas, but thinking of Georgia) are religious based and many are nonaccredited. Most of them have very, very small student bodies, which are great for one on one time but not so great for opportunities to make friends and connections.
The school which my husband attended was a nonaccredited private Christian school and his education was horribly inadequate. His biology 'teacher' spent more than an hour arguing with me over whether or not insects were animals (the man had an associates' in architecture) and his diploma was more or less worthless.
A friend attended a small private Christian school, graduated at 15, and went to Georgia Tech on scholarship. She had an enormous advantage over me when it came to opportunity, but a disadvantage socially.
At public school, which was frankly an underfunded, very small yet very crowded district, I was able to obtain an excellent education. I found that, as others have said, the staff made a world of difference in the quality of education available.
Thanks to the generous teachers, who gave their time, money and expertise, our very poor district had football and other sports teams that competed and were comparable to the teams in wealthier districts. In addition, they had a wonderful livestock showing and agricultural education department and a terrific band.
The drop out and preganancy rates were high, but a good teacher just opens the door. The student has to walk through alone. The quality of the education I was able to recieve for free at a public institution was very high.
The people who failed, scored poorly on tests, and dropped out had the same opportunity to learn and excel that I did. I understand socioeconomic pressure, but I didn't grow up in Shangri-la.
I think that people who are going to take initiative, learn and succeed are going to be able to get as good an education at a public school as at a private school, but a student who may not be motivated to excel may do better in a private school where they can recieve one on one attention.
However, one wonders how that will transfer into college and careers, because while one on one help and attention can help a struggling, undermotiviated student excel, no one will be there for that after high school.
Another point (I know I'm rambling) is to think of the money. Even if you live comfortably and the extra expense won't strain you, would it do more good if you put it in an ESA or otherwise invested it to give to your child for college?