Just following up my earlier rather dashed off comment. I should have started by saying well done to your DD. Either will be wonderful! She has done well and is so lucky to have the choice. I didn't really mean single sec is better for girls in terms of results (have no idea on this) but in terms of personal experience, breadth, opportunity and range of challenges accesible, acceptable and available. I went to a girls' school and so did my daughter so I am obviously biased - but I know far more girls did maths and sciences at those schools than at mixed schools. Equally, at my sons' school, more boys did English, drama and art than at mixed schools.
My DD loved every day at SPGS and has a very strong friend group still from there. They are based all over the world but travel to meet up regularly. But more importantly, she did so much and felt so free to explore things without any male gaze on her. She was shocked (as was I) when she encountered dreadful sexism at uni (she was doing science) and so many of the male students treated her as lesser because she was a girl. One famously said to her "you can't be doing Physiscs, you're wearing hoop earrings". She was, and she did fabulously, but grappled with dismissive male students and supervisors throughout. Shocking!
You could argue it would be better that she was exposed to that beforehand, but actually for me I was happy she had had all those years free from it. And she has brothers so I knew she wasn't growing up without any experience of the wider world. She had and has good friendships with lads from SPS but I think is very glad she was at SPGS. She did music, sport, drama, dance - some well, some poorly but all with great joy - as well as her academics. It was a very rich time.
She did explore the idea of Westminster for sixth form but decided her teachers for her subjects were better so didn't pursue it in the end.
Good luck with the choice xx