Honestly, I believe it depends on where you're from. For instance, I live in Baton Rouge, Louisiana. Not the safest place to live. At all. If you attend public school here don't expect any kind of decent education, but you can expect the necessity to carry a knife with you.
Personally, I've attended private school my entire life. Yet, just like with anything; there's the good, the bad, and the ugly.
If you're looking for "more bang for your buck", private school is the way to go. If you're looking for something that'll get your kids to college, public school is the way to go.
My family and I are about to move to Bentonville, Arkansas. They have a magnificent public school system up there, which I may or may not decide to take advantage of.
When it comes to the quality of schools, whether it be public or private, it's always about location, location, location.