As @Walkingtheplank has said, I think pretty doubtful that there will people with experience of both schools.
WHS is rather academic and, on a quick look, the results are strong than for the other school that you mention. A key difference is the fees (not sure what is your financial situation, etc) and, even if you are in rented accommodation, surely where to live is a major issue, not only in terms of preferences but also of cost. And I assume that there may differences also in terms of curriculum (e.g. MFL on offer, GCSE options, etc), not to mention the extracurricular.
Focusing on WHS, which I have direct experience of, it is a great school, with strong academics and pastoral, a wide and inclusive community and a very strong extra-curricular offer. It is quite progressive in terms of the teaching with a big focus on DDs' responsibility. Quite a few girls leave after GCSEs, mostly those that have been in single sex education since age 4 (and especially in the same school), almost all to super-competitive co-ed, like Kings College Wimbledon or Westminster, which is a sign, in a way of the high standards of the school. There are quite a few posts about it in different threads which I would encourage you to read.