I can't comment on S & C as I have two boys, but I have very long experience of Thomas's Clapham. My elder was there from 2005-2014 and my younger started there in 2011. It is absolutely not the case that they do not 'develop the whole child'; both boys have done huge amounts of music, drama, sport, public speaking, art, creative computing, etc etc. The school actively develops children's self-confidence, but at the same time encourages them to think of others and give back to their community. I think they produce well-rounded, non-arrogant kids, with good skills of applying themselves to their studies.
I remember being anxious before my older boy started there, after having been warned of 'hothousing' by other parents (notably whose kids hadn't been offered a place!). It is an academic school and it is busy, bustling and full-on. Your child(ren) need to be robust enough to thrive on that. However there is not a 'Thomas's type' - the children are a good mix of alpha-achievers, normals and those who need a bit of extra help. The parents don't conform to one stereotype either.
If you hear opinions from other parents, be wary of those before 2013, when the Head changed. The current Head has very different views and has brought in many excellent changes, mainly about building good life-skills and attitudes. He has also encouraged much greater diversity in where the children end up afterwards, either at 11 or 13+.
I suggest you book visits around both schools again and try to picture whether you can see your daughter there. Look at the kids there; is that how you'd like her to develop and the sort of friends you'd like for her? Lovely to have the choice - but tough too! Then go on your instinct - good luck!