I'm guessing it depends on the area and schools?
In our area, Middlesex, the kids who went private are the ones who didn't manage to get a place in the selective state schools in the Sout West Consortium , QE boys and Henrietta Barnett.
The girls who went private ended up in schools like Goldophin and North London Collegiate but when reading posts on here it looks like the independant exams are much more complicated than the state ones.
Is there just more competition for State places as you don't have to pay?