As said above, it depends on where you live.
There are literally hundreds and hundreds of very, very high level public high schools in the country.
Best High Schools in the US | Top US High Schools | US News & World Report
Of course, there are thousands and thousands of really bad public schools, too.
I live in an area where the public high schools are very high level. Some kids go to private (many for religious reasons), but the majority, including those from very high income families ($2+ million house neighborhoods) go to the public high schools.
Some actually send their kids to private for *lower* academic standards, b/c the public school they'd have to go to (based on where they live) is so cut throat competitive. The theory being it's better to get a 3.8 at an easier private school than a 3.2 at the hyper competitive public school.