I don't know anything like enough about G and L to comment though clearly it's a great school.
However younger DD is at SHHS and overall we are extremely happy with it. She is now in year 10 and is well on course academically and, more crucially for us, as she wasn't hugely confident at the end of primary, the school has been very supportive of her. Her talent for creative writing has been nutured (far more than at other schools I could but won't name!) and I was amazed that in year 7 she read her own poetry out on speech day, and has done subsequently, and also has sung solos at the teatime concerts. Quite something given where she was.
She has several groups of very nice friends, and seems to move easily between them - there is a bit of friendly academic rivalry between them but nothing to cf with some other schools! That may hot up as we approach GCSEs but until now, although I think there's a bit too much testing, the school seems to be building confidence and some of the teaching is very inspired. Big emphasis on books and literature which we like.
The music is excellent - esp the orchestras and the chamber music - great big band and very good choir in the early years. I am less happy with the senior choir, but otherwise it's great; there are some incredibly good musicians amongst the students, who get a chance to shine - including a couple of chamber groups who are performing regularly at Wigmore Hall etc. There's a wonderful concert each year in St John's Smith Square which is very inclusive (though long as a result!) Equally important there are a lot of groups for the less able and the tea time concerts try to include everyone as far as I can see and are a very friendly and supportive way for new performers to perform. Always attended by the senior staff which is nice too.
I can't comment much on sport having very unsporty offspring - but there do seem to be lots of girls in tracksuits and lots of coaches going to matches! It's more part of the fabric than elder DDs school.
Not sure if they win or not.
Overall it hasn't felt as pressurised to date as other schools and I'd say individuals manage to be themselves largely. Of course it's not perfect - but no school is!! And it will go through a bit of turmoil with the building work - but for any girl joining now, that won't matter. It's not so good for us but does need done.
Do pm if you have more questions. Good luck with decision - and do go back and see the schools - they look very different when you have an offer.
And while I'm here, well done to everyone with offers! PHEW.