I think it used to be true that you could buy a better education through a private school. I don't think this is the case anymore.
Private schools can be less bad. Around here (Bay area, CA), public K-8 schools have short days, except on Wednesdays, when they have very short days (the kids go home after lunch). Private school buys you a school day that lasts until 3 or 3:15 every day, and no furlough days. Overall, this translates to one extra day per week compared to public schools. So they have ample time for things like art, music, science, and so on. They also have time for field trips (Alcatraz, the Beethoven museum, and a local art museum, for example).
Of course, my public school education in the 70s and 80s looked just like this.
At the same time, a lot of private schools still fall into the same bad thinking that hinders the public schools: fad mathematics, every child is gifted, rigor = more homework, and so on.
A guy who grew up around here once told DH and I not to spend more money on a smaller house in a better school district because the success of the district was due to the parents more than to supposedly exceptional schools. Now that we've lived around here for a while and now that our eldest is a bit older (13), I see what he meant.
In contrast to a few other people here, I do think it's possible to judge the US education system as a whole. This is primarily because of our consistently mediocre results on international exams like the PISA, the watering down of course content, the watering down of high school exit exams, and the high number of students who end up taking remedial classes in college. Sure, there are some good schools out there --- but there are more good parents.
