It was me wondering if this is the influence of the new Head at KGS, from Aylesbury Grammar a state boy's grammar, so not much experience of overseas candidates and more experience of a first past the post system. I would imagine state Grammar School Heads find the mandatory and economic restrictions they face on admissions arrangement frustrating but it must make jumping from that culture a little more difficult. Sarah Fletcher came from a very different background and she changed an existing culture. I just hope that it doesn't mean a change in ethos since that popularity as "ecole de jour" mentioned by Needmore rested on reports of happy pupils and encouraging teachers focused on individual potential as opposed to it being focused on results and rising up league tables, far too much of that around.
However agree with Dino that harder papers don't necessarily equate to harder to get in, that depends on demand, and actually 700 sitting at KGS, and 400 at LEH isn't an increase on ten years ago, although there would have been a dip in numbers a couple of years ago when an unusually small cohort came out.
Also what is "harder" in Maths? Most schools try to have questions that apply familiar questions in unfamiliar ways to test logic and reasoning skills (especially the more selective ones who want to distinguish the bright from the tutored) as well as straightforward questions, some pupils will find the former easier but may not be good at being accurate at the latter, some the other way around. And in English there is even more variation between the different skills that a pupil can display.
By the way whoever said that LEH take a low proportion of state school applicants were being a bit unfair, the Prep skews it but if you take the non Prep intake about half will be from state primaries / overseas. However it is very focused on ability and talent, hence the general paper and focus on interviews, and can be most selective from a very wide catchment (larger than pretty much any of the schools, Ealing to Ascot, Cobham to Windsor) so individual primaries won't see many get in, so it is just a very high bar.
Basically I think it is impossible to speculate on what these schools are looking at /for without talking to the Heads or failing that seeing the papers, and who turns up in the schools afterwards. Having done all that I can only say that the Chinese whispers in playgrounds often don't help. I hope as is usual that less selective schools like St Catherine's and Surbiton ride to the rescue of the disappointed, the vast majority of parents of pupils at both schools I know are very happy with both.