Thanks for your DM, OP. Thought I would reply here as there might be others similarly situated.
To start, I agree that there's no wrong choice - both schools are excellent academically (and probably your D's current school as well).
It was a very difficult decision for us but in the end we chose SPGS over HBS. We asked our D which one she preferred and she didn't express a strong view to me, although I learned later that she had mentioned to my SO that she liked the "greener" feel of HBS.
We were not keen on paying SPGS fees (200k+ over 7 years) but didn't want to short-change D's education for this reason (in the end, I think we had arrived at the view - partly informed by people familiar with both schools, including 1 or 2 who had attended both - that SPGS was the stronger school academically (beyond public examination results)).
At the time, I was also concerned about government ministers' tendencies to tinker with state schools, sometimes seemingly based on whims rather than on robust evidence and I thought that a private school would provide greater stability.
Our D stayed at SPGS for 7 years but developed mixed feelings toward it over time, partly due to the intensity of an all-girls environment (in that sense, this could have also happened at HBS) and partly to the way a certain department was managed. But I think she would acknowledge that she received an excellent education at SPGS and was particularly stretched (in a positive way) by her "OP" (Old Paulina) teachers.
One worry that I had about SPGS going in was that our D might struggle to keep up (she did not attend an academically selective primary school) but she coped fine and didn't need any extra tutoring during her time there. What I think is a bit sad for most SPGS girls (my D falls into this category) is that they are often overshadowed by a few "superstars", whereas at most other schools they probably would have received greater recognition. As a result, a good number seem to leave SPGS with unwarranted insecurities about their abilities.
In retrospect, I don't know if we had made the absolutely "right" decision. Having said that, I am grateful that our D received a top-notch education at SPGS and, importantly, could be her quirky self there without being ostracised or bullied (that was another of my worries). Perhaps she would have done equally well at HBS - and, as an aside, we actually feel we would probably have meshed better with HBS parents - but we will never know...
If you are really on the fence, I'd suggest choosing HBS now and seek a transfer to SPGS if things don't work out as hoped (this seems easier than the reverse).
Best of luck with your decision!