Hi OP. My three kids all went through senior school at Cheadle Hulme .. they passed for both schools but we went for CH largely because of how much we liked the atmosphere and the teachers when we visited on Open Day. Very approachable and not afraid to have a laugh with parents whereas at SG they were a lot more "careful" about how they came across. This was over ten years ago so could be quite different now of course.
Academically they are pretty equal I think, so it comes down to which school will suit your DD best. Stockport in our day seemed more traditional and maybe a little stuffy but that may have changed now. CH seemed to be a bit more fun and imaginative with their extra-curricular activities. In later years my DD was a "spirited" teenager and they handed her with good humour .. I was extremely impressed.
We had some ups and downs with head teachers but now CH has a woman head, ex cricketer for England, who happens to be gay and I hear really good things about her.
The senior leadership team was always excellent. If you visit again, try and have a chat with Sally Petrie (especially if she is still pastoral head for Y7) and John Winter, who was head of sixth form when my kids were there, and I think is Deputy Head now. I have a lot of time for both of them.
By the way, my DD was also very bright and stood out as such at her state primary school. Once she got to CH she fitted in very well with a lot of other bright kids and was actually much happier.
A few random observations .. HTH 