Hi OP, what a lovely choice to have!
Disclaimer: DS is at St Olave’s and DD1 is at NW - years 11 and 9. I have friends with daughters at Bullers Wood.
From my point of view, both my kids’ schools suffer somewhat reputation-wise on line, and I remember how worried I was when considering them both. Exam factories and poor pastoral care were concerns raised by many posters. (Not usually 1st hand experience.)
Now both kids have been there a couple years, and with many friends at a variety of SE London and Bromley state, academy grammar and indie schools, I realise how anecdotal all of this is (whilst sharing my own anecdotal opinion now 😉). Some parents have loved Kingsdale, some have not. Some have loved Langley Girls, some have not - my 1st born had a pretty poor time at primary school, my other 2 have really enjoyed it.
Back to your post: I have not found NW (or St O) to be an exam factory or poor on a pastoral level. They are both quite quiet, rather shy, and can be anxious - I contacted St O in y7 and NW in y7 and y8, and they were amazing: support from form tutor, head of year, head of pastoral support, etc etc. Both schools are aware of their on line reputation, and I think are addressing it in a very real way: St Olave’s even has a well being cockapoo now!
I am not thrilled with the quality of some of the teachers at NW, their ability to hang on to them - or communication with parents. St Olave’s is a much much slicker operation.
DD is very happy there, doing really well, and that’s what counts, but I am slightly underwhelmed.
My friends’ daughters are doing very well at BW, very happy there and I hear that Buller’s wood’s extra-curricular activities are very good too. But then my friends with children in the same year as DD are perfectly happy with NW - it’s so hard for schools to please everyone.
Good luck with whichever you go for.