Which one do you live closer to? QG tends to be more of a Knightsbridge/Chelsea sort of demographic. SJ is further west. I’d start from there, as the social fit, while less important in early years - does become more important as they grow up.
I heard more good things about QG than St James. Also there seems to be quite a different subject choice in GCSE and Alevel in two schools so have a look at their syllabus. I prefer the Queensgate subject choice