Regarding MC children I think there's a similarity with private school but generally I think they do have a harder time at State school. Most have two parents working full time and can't supervise homework or revision - this is where private schools I think step in to ensure children aren't slacking off. And they are often left to drift at school because state schools think they're doing OK because they went in with higher levels at primary
I think there is a lot of truth in this statement. Our local school is rather poor in my honest opinion, but most families are MC and with a SAHM who does intense tutoring/supervision etc.. and the work the children produce is amazing. Unfortunately this set up does not benefit the children like mine who have 2 parents with busy full time jobs and don't have the time to do any tutoring, neither the few ones with parents who do not have the skills to do this either. These tend to be the children who struggle the most and the older they got the more they are left to drift.
This is one of the reasons I switched my DD1 to private school. (Still have other children in state but they are younger).
They do a hell of a lot more at school and the results are probably the same, expect I pay the school to do it all for me and I don't have to worry about it. In all honesty I do not have the patience or the skills or the time to teach my children academic stuff anyway and the little time I have with them I would rather do fun stuff than sit down with a workbook. (They do get homework but it is always tasks they have already done at school so can be completed very quickly and independently, as opposed to what we used to get before, which was complicated stuff they had not been explained at all and there were always tears and tantrums).
I also spend quite a bit of time doing musical activities with the children as this is something we all enjoy together and we found we had less and less time to do this.