I've seen both sides. The majority of state education is poor, but to be hoenst, the majority of state kids are arseholes. Go to a nice school like the one in Leicestershire I've just finished at, or where my wife works now in Warwick, and you'd hardly notice the difference outside of the bottom sets in terms of quality of work in the classroom.
The better education comes form having more motivated kids, being able to kick them out at will, better funding, more motivated parents and smaller class sizes. Though having said that I've seen some fucking shocking practice at private schools that would get shut down in minutes in a state school. I remember we had one teacher come from private (both as a student and teacher) and was shocked when we told her she couldn't help the kids during their exam ("Oh, we always cheated at Henry's"). Cheating is rife as the parents pay for the grades and don't expect to hear "No". That said, until fairly recently cheating was becoming rife in state schools as well as there was so much pressure for results.
Kids is kids. Teachers is teachers. They all come from the same place originally, there's no special sauce because it's private.