I went to a private school for 12 years of my school career, and moved to a state school for the final year of my education.
Something which always bothered me was the snobbery when I was at the private school along the lines of: "we have better teachers, therefore better education". Teachers are teachers the world over. You'll get teachers with different teaching methods, and of varying qualities. Some that you'll like, some you won't. But I found this has absolutely nothing to do with the school; it was to do with the teacher. A private school teacher isn't necessarily better than a state school teacher. In fact, from my personal experience, I found the teachers at the state school more useful to me with regards to extra help and going out of their way to best go over stuff to the class.
I disliked at the private school the fact that there were fewer opportunities to get involved in extra-curricular activities such as sport and music because they were elitist (looking for the top 11 football players for the team), or looking for a certain thing that you couldn't offer (only wanting classical pianists, rather than jazz guitarists etc). When I moved to the state school, there was endless opportunities to be involved with sports teams, and getting help to improve, regardless of your ability. School concerts operated on a kind of 'showcase what YOU can do' basis, where everyone got their opportunity at least once throughout the year. I found this refreshing, and actually allowed people to grow in confidence and develop skills out-with their studies (something which I think is important to receive a rounded education, an be prepared for later life).
What I would say is the private school did have a less interrupted education for the lower sets, as they had the right to expel/reject placements of students who were going to be a problem in classes. However, I didn't experience the full disruption these pupils would have caused, because I moved to the state school for my sixth year of secondary school, by which point most of these problematic pupils had left.
I'm aware this isn't an argument for (or against) the abolishment of private schools, it's simply the opinions and observations of someone who has been to both. I personally feel that a state school offers you the opportunity to escape the private school bubble, and see real people and therefore be more prepared for life after school.
While I preferred the time I had in the state school, I understand that there are people who are more suited to the private schools too. It's personal choice, I think.