We, without thinking it through, have brought our children up in a very success orientated part of Britain - Central London. As well as attending academic private schools, DC have attended a number of out of school activities. For some children, the pressure to excel is huge, and certainly till about 13 or so, the affluent ex-pat kids, with what might be described as Tiger Moms, seem to perform better than others. After that it seems to even out. If you don't find chemistry or maths easy, lots of tutoring might get you to GCSE but not much further. Ditto with sport or music. You can be technically very good but at some point natural talent shows through.
Some of these kids then have trouble adjusting. First to having to find their own drive and initiative. (In one or two cases you wonder if the mother plans to accompany them to college.) Second to not being the best. In all innocence other girls once pondered how DD could have achieved a gold in Junior Maths Challenge when she is not at the same very academic West London School that they attend, and indeed, as they pointed out, she is not even at the two or three schools that they might have considered as fallbacks.
Team sports, orchestra etc are good. If the school asks you to play, even if you are not the best. And the team captain will expect other girls to be kind to the last minute reserve, even if she did in fact "let the team down". There is a lot to be said for the playing fields of Eton.
Not just that but the medical evidence that suggests that being active when you are a teenager means stronger bones in later life, plus lots of oxygen in your blood stream may be good for brain development.
The activity my daughter enjoys most is the one where she is the only private school pupil. The other girls are committed and get on with things, but without the need to prove they are better.
Both DC have enjoyed their education and have good straightforward friends, but if I were starting again I would look more closely at the likely peer group at any school, perhaps looking for a wider willingness to participate. To us the willingness to try your best, even if you are not much good, and for that to be acceptable to your peers, is as important as being the best. The prize is potentially a life-long enjoyment/appreciation of sport, music, art or drama, a really valuable gift.