First of all congratulations to your DD - a wonderful choice to have!
We had exactly that choice last year, for a DD that seems very similar to yours. We really liked both schools (they are were our top choice) and, like you, there was no strong preference for co-ed or single sex. We opted for WHS on account of a number of factors, including logistics, smaller cohort size, curriculum (quite liked the GCSE options, including 9 GCSEs plus sPPE, and degrees of freedom on choices), the facilities and proximity of the sport fields. Academically they are both strong but WHS probably has the edge.
DD is now Y7 and we have found the school really good in terms of balance between school and other activities - homework is not much and the DDs really learn early on (with guidance from the school) to organise themselves. Most clubs are at lunchtime apart from some music and sports and the school is very aware that the girls pursue a range of extra-curricular activities outside school hours so no homework is due form one day to another and when there are 'only' 2-3 days, it is quite minimal. There are also indications of how much should be spend on pieces of homework - that I think helps address the perfectionist streak of some girls. There is no homework during half terms or holidays. Our DD has been very able to combine the school and homework with all her other activities (singing and 2 instruments, as well as out of school sports) and has not pressure, and she has plenty of friends with significant out-of-school commitments (including sports at county level) that, like her, feel very able to combine school and the rest. The teaching is very interactive and quite a lot of the homework is focused in ensuring that the knowledge is anchored through discursive learning / presentations.
The school is strong on the pastoral element - even before they started and in the first week there were lots of activities for girls to meet each other (both within and outside their form) and get to know each other, including a lovely weekend residential. The houses structure also helps to make friends both within and beyond the year, as do the clubs and, at the beginning of the year, each girl is assigned a Y8 buddy. It seems that it has been quite easy to make friends and the school has made sure that DDs are really mixed (i.e. not having girls that 'came together' grouped in the same form) - and in addition to taking some lessons with their form, they are in different groups for languages and maths.
Overall, we have had a really positive experience so far.
By all means, feel free to PM me if you want to ask any specific questions.