My grandkids are homeschooled, one of my daughters goes to a private school, and the other goes to public school. They are all doing well!
I am a middle school teacher and our kids get a GREAT education at my school. The teachers really care. But there is a lot of stuff that goes on with the kids that stresses me out. All kinds of kids just thrown together.
Private school - expensive. GREAT education. Motivated students. Not much room for differences
Public school - free, Education is what you make it. The teachers are there and they work their tails off, but you can't MAKE a kid want to learn. IF your kid is in AP classes and wants to work, they can get a GREAT education
Homeschool - has room for LOTS of creativity. Depends on how structured the parents are and how dedicated. Works great for some and not so great for others.