Now, encouraged by @poetryandwine 's post I have read back a couple of pages.
There is a great variety within sectors, and a great variety within schools. DC's sixth form (one of the big names) really encouraged pupils to show curiosity and acquire independent-learning skills. At the same time, and something we only discovered later as it was not as common within DS' particular friendship group, was that there was a lot of tutoring going on, both to get into the school and to keep up once there. Admissions officers might then have wanted to split out the naturally curious against the heavily tutored, which would not have been easy. Small sample, but DS' friends as a whole did very well, with most staying on for Masters if not PhDs, even though most studied in London rather than Oxbridge.
The school were keen to discourage complaints about unfairness when it came to University entry. They had had an advantaged education. But parents were not convinced, and with an increasingly international parent body, more went overseas. The broader education and expectation of taking part in a range of activities appealed to US University recruiters, whilst Canada, Italy (Bucconi), Ireland, Netherlands, and Australia started coming into the mix.
My DC are now a decade beyond school, but like many of their peers, are dealing with the challenges of the current job market. Getting good grades through school and University are important but not enough. Resilience and resourcefulness, communication, problem-solving, interest in acquiring new skills, being a team player and a lot more.
This, as poetryandwine suggests, seems to apply to medicine where poor NHS management seem to have decided to do away with merit as a selection criteria, or use it in an odd way. (So more points for published research or for competitions won, but no scrutiny of the quality of those publications or competitions, one reason why more international applicants were getting onto training than UK educated applicants despite many or the latter never having visited the UK let alone worked for the NHS.) 50% of DDs year group were unemployed at the end of Foundation 2 last August joining a large existing bottleneck of underemployed or unemployed doctors. Bizarrely after six weeks of nothing, she got to replace a consultant equivalent (Specialist Associate) in quite a niche area responsible for a couple of dozen very sick patients and supervising half a dozen first year doctors (F1s). Four locums had left quickly but she somehow survived six months (on a zero hours basis at half the pay of the post holder) and would still be there if she had not moved to Australia.
Her experience probably reflects the complaints of the consultants poetryandwine refers to. Looking back DD's survival was as much about skills gained outside education, as within it. Obviously good medical knowledge is important, but resilience, assertiveness, empathy, teamwork (she had a strong team of nurses), an ability to think independently and not to sweat the small stuff, were crucial. Sport, a season as a chalet girl, and her school leadership role all came into play. The same was true of her F1s. (Very NHS to get a locum with no assessment training to write appraisals - in the end she told us what she wanted to say and we suggested language.) The majority were fine, some very good, but amongst the group there were issues with anxiety, over-confidence or lack of attention to detail, all unrelated to prior academic performance. (The same will be is true of doctors recruited from overseas.)
Medicine is a bit extreme, as it can be life and death. DD ended up sounding middle aged. "Think, don't just ask me." "Get away from the computer and observe the patient." and so on. But in an AI driven world, wider non academic skills are bound to play a larger role. So my answer to OP would be to think about where the DC will get the better and wider education.