Your education may not be as personalized and your class size may be large. The desks may be older and the cafeteria may not be as nice. However, in terms of education, there are many public schools that compete with most private schools because they're in nice neighborhoods and can guarantee a safe learning environment. That attracts a lot of the best teachers and enables a lot of students to be able to do their best. It also helps that fundraising for these schools isn't that hard, and they often don't have to spend extra money on things like metal detectors as some schools have.
I went to one of these public schools. My family was middle class, but some of my classmates were f*cking wealthy. I parked my 1996 Toyota Avalon next to a new BMW because she was the daughter of some rich CFO. Our school has a few assigned parking spots, half of which you can win through a $5 lottery ticket and the other are auctioned off to raise funds for the band (or something like that). I always found it hilarious that while I paid 10 or 15 bucks for my front spot, the girl next to me had her father pay literally a 4-digit figure. That one spot paid for a lot at our school, and raised more than a car wash fundraiser for another school might've.
The really rich private institutions are the exception. Public schools that cater to wealthy students can't even compete. They don't have the manicured gardens and the catered meals. Their students dress nicer and may have access to more subjects or other extracurricular pursuits. They're also expected to perform at the highest academic standards...however, the education at these public schools are still rather good so they're attractive to parents who rather fund their kid's college fund with what they save.