I said potentially mediocre because I realise that this is not always so.
As it happens, in all the activities that my children excel in, their 'out of school' provision attracts children from the local private schools, who have 'done that activity' at school. Again, as it happens (and I appreciate that this will not always be the case), those children are well behind the children of the same age who have attended only the out of school provision.
Which is why there is no one answer to 'state vs private'. Locally, the state schools are better than the private ones, and state school + community provision for out of school activities better still. In other areas, that position will be reversed. It is as absurd to state that private education is always better as it is to say that state education is always better. It depends entirely on the precise schools concerned, and on the child.
If my children were very gifted at polo, the private school is the best place locally to do it. As it happens, their gifts are in classical dance and football, and in those cases the provision out in the community is much better. Equally, my children are academic, and thus better catered for in the state sector, as the local private schools are placed lower in league tables and university entrance tables than the state schools. If I wanted them to meet only the children of Russian oligarchs none of the hoi polloi, then they would be better catered for in the private schools.