I would agree that at 11+ it's harder to get into some if the super selectives than the very popular independents, in terms of applications per place or the fact that many children seem to get offers from the independents and not the state super selective.
For those who can pay for the fee paying alternative, certainly in London and the south-east, there are lots of independents which outperform the perhaps more selective state super selectives. If you look at The Times Parent Power tables for A/A for both independent and state schools, far more independents are in what is called the 90% club (90% A-B at A level) - I think perhaps 45, compared to 10 state schools. And there are similar patterns if you look at the 80% club too - so those fee paying schools, some of which are very selective and some significantly less so, in terms of applications per place, seem to be adding lots of value.
Outside of the southeast, the trend is not so clear cut. Because many private schools are under-subscribed they are far less selective and their results reflect this.
If you get a place and QE boys and HB girls, or the Tiffins or a handful of other superselectives, then yes, those schools appear competitive with the very very best. Many other superselective state grammars are still clearly doing a great job, but their results are lower than many independents, and if you look at the non super selectives in areas like Bucks, again the results are great but nowhere near as great as a good number of independents.
Certainly there's kudos in some circles of being able to say your child passed for QE boys or Tiffin, but actually if you live in those kind of areas and have money to pay fees and a pretty bright child, even if your child can't beat off 1500 other applicants for a place, they can get a top education and do as well as those kids in the end in lots of independent schools. As has been said before, people who know they can pay fees, perhaps don't invest quite so much in the preparation in terms of crazy efforts, because they have a number of options - perhaps these kids aren't quite so bright, but they are bright and given he right education can be huge successes. And people who can pay, often like the fee paying schools broader focus which meanies them at least seem to not quite so much exam factories (although to be honest, all those schools in the 90 and 80% clubs will be exam factories to some extent). If you can't pay and know scholarships are usually fairly small amounts and that you won't qualify for a substantial bursary, the incentive to prepare for those super selective state schools is greater, no doubt about it.
Who knows, in the end, perhaps all of the kids in those London/south east selective state and fee paying schools are of similarity ability - they are all bright, but it's the extent of tutoring and preparation that gets the bright into the super selective state schools or stops them getting the places. Perhaps the similar ability explains why the independents can deliver similar or better results??