In which case, my three-penny-worth.
Westminster has a very strong track record for US applications. Don't know how it compared with SPGS, but I would be surprised if it weren't as good.
Westminster appears to be a very different school to SPGS. As long as you are not struggling academically, and sixth form entrants should not, it is surprisingly relaxed. Pupils work hard, but that is the norm and because education is seen as something to engage in, not seemingly because they are under pressure from teachers. My son was very happy there, and has done well. However it might not be a school for a pupil who lacked self-motivation, as there is quite a lot of onus on the individual student to organise themselves.
DD is not at SPGS but knows a number of girls who are. From the outside at least there seems to be a lot more homework and testing. She has been surprised at times how the girls will describe others as "not very bright" and how seriously they seem to take things like scores in Intermediate Maths Challenge. Most of the girls DD knows at SPGS are very happy there. A few are not, and indeed a couple have left.
If your daughter is doing well where she is and happy, she should probably stay.
If she is doing well but not particularly happy, Westminster is really worth a try. As you will have spotted from the boys you met, it is quite laid back. The sixth form is special. It operates as a boarding school, so open long hours, so scope to study in the library after school, have dinner and then go to the gym. Class sizes are small, which combined with bright pupils and good teaching makes for good results. Equally though, the other activities and the expectation that you participate in, say house competitions and performances, gives a rounder traditional public school edge. In my view it provides a great preparation for University and adulthood, and it was lovely to see my son and his friends develop and mature over those two years.
I understand that only a handful of girls made the switch last year, whereas in DS' year about a dozen moved. DDs friends say that this was because SPGS was top of the League Tables, having passed Westminster. If true, I find it sad that a decision of two outstanding but very different schools would be made on the basis of League Tables and raw results, not on the quality of education and the fit.