Ok, here some feedback from a " private school parent".
I moved my children out of the state sector a year ago, and am now looking for secondary schools (state or private) for the next stage.
I am not into the whole status thing, old boys network or anything like that ( younknow, I would liek to think we are not that sort of parents).
We were disappointed with our state school, due to class size ( 36 in Y3), lack of SEN support ( they did not even want DS2 tested, due to cost?) , but mostly the ongoing low level disruption, which created an environment in which it was difficult to learn. I helped out in the classroom, as teacher was desperate and no TA in Y3, and I was happy to help.
It was an unexpected eye opener, it was just all so chaotic, noisy and kids constantly getting up and walking about and chatting.
What I am paying for now, is really " classical teaching", ie a teacher in front of the class, all pupils facing the teacher, the teacher removing unruly children to go and see the HT if needed. There is more time for learning as there is less of a need for crowd control.
Some would call this approach "old fashioned" though, and it is not at all n line with modern education theories of lots of group work, and teaching kids to cope with disruption etc. interestingly there are 5 children with SEN or SN in DS class, they get one on one support daily if needed and in classroom support. Some of these kids can be disruptive, the parenst then get involved.
It is not nirvana, just a bit less chaos and discipline, and most importantly, higher expectations of the children.
Low level disruption and low expectations ( being told after y2 sats that my Ds was bottom of the bottom set, and that in every class someone has to be bottom, yet refusing to assess him for SEN, telling us he would never get to level 4 by year 6) as well as lack of SEN support made us move.
For state schools to be more like this kind of private school, they would need more money and for parents to be really on board regards discipline. Neither are very likely to happen, sadly, due to lack of funds and a changing society where people think their kids do not need to respect the teachers.