I went to an independent girls day school - when I was there it was generally top of the league tables for exam results (although it's now down out of the top ten nearly 20 years later), so it was a very high achieving, high pressure environment
I absolutely thrived in this environment, because they didn't just drill for exams, but taught me how to think. Because the academic standard was high, and everyone was expected to get top grades (anything lower than a B was a massive outlier), they basically got the exam syllabus out of the way as quickly as possible, to spend more of the lessons on stretching us intellectually. If you were struggling then there was absolutely no hesitation in giving you extra coaching you needed to get you where you needed to be. I remember for A-level history spending time on lines of enquiry and debate that had nothing to do with the syllabus, but which were the best preparation for my Oxford interview and degree than I could possibly have imagined
I genuinely didn't realise that getting into Oxford was as big a deal as it was perceived to be, because there were so so many people who got Oxbridge places. I think bar one or two people, everyone in the year went to RG universities. There was very much an expectation that we would go on to be high achievers and captains of industry etc. The school was founded in the 19th century to specifically give girls a strong education in STEM, so there was no sense of anything that girls could or couldn't do. We were encouraged to be free thinkers - no one cared if you came in with piercings or punky hair or what you wore (no uniform in sixth form), it was your contribution that mattered.
Competitions for 'young analyst' (national chemistry competition), maths Olympiad, model United nations etc were standard. I did public speaking and debating competitions, as well as on the school general knowledge quiz team. So even though I wasn't sporty or musical, there was plenty to do. We also had to do an afternoon of volunteering in the local community in sixth form - again I'm sure this was for UCAS forms, but it was a valuable experience to have that part of the timetable.
The down side to such high expectations was that there was a very high incidence of eating disorders - probably a quarter of the year had some degree of ED at some point, some spent quite long stretches in inpatient units. There were a few cutters (self harmers) as well, I think. I thrived in the atmosphere, although I think Oxford was a bit of a shock when I was no longer sailing through with quite such ease! It did leave me with a very strong sense of competitive spirit, and I can be quite tough on myself if I'm not performing to the standard I expect of myself. I do remember feeling relieved that I had got the 9 A-star GCSEs I'd hoped for (still quite unusual in 1997) but deflated that it wasn't as impressive as the handful of girls who'd got 10 A-stars, because they'd done extra subjects in their lunch hour or out of school
I've no experience of state school to compare, but I adored my school experience and feel it equipped me with so very much more beyond academic grades that I use in my everyday life. But may very well be saying the same if I'd gone to the local state grammar instead!