What you pay for in private education is small class sizes. (Don't be misled by 'pupil teacher ratio,' that's a different thing.)
The quality of teaching, in my experience, is no better in the private sector and a lot of teachers seek refuge in private schools from 'lion taming' in inner-city comprehensives
It's easy to teach compliant pupils with supportive, fee-paying parents. The best teachers are those who get good results teaching in 'difficult' schools.