This is a really complicated issue and I guess it really depends on your background and ideals.

Homeschooling lets you control the curriculum and helps your kids expand into the directions they are naturally good at. The problem is that the parents have to be very attentive and also supply a social environment for the kids so they are not cut off from other kids their age.

Private schools are sometimes like a cocoon that shields from the outside world but gets the kids into less life building experiences.

Public schools really differ from each other since they may be good or bad depending on location and profile of the neighborhood they are in.