VSVQ, I think some of your points are valid when applied to Alleyn's vs City, but I would disagree when comparing City to JAGS.
Academically, City and JAGS are identical (with JAGS outperforming on some subjects, City on others, similar numbers to Oxbridge, etc). If anything JAGS probably has better teaching/gets more out of its girls as it gets these results with slightly less selective intake (~480 applied to JAGS, 800 to City and no "puzzles/maths" interview at JAGS).
Values/culture similar - both very multicultural and, I assume, socially diverse. I don't know about City but JAGS has 20% of kids on bursaries (which are on average 89% of fees). If anything, JAGS is probably more diverse because it doesn't have concentration of specific ethnic groups (like Jewish/Indian at City, Habs, NLCS).
JAGS has better facilities and fantastic language provision (comparable only to SPGS) with Italian, Japanese and Russian offered. I think SPGS also offers Mandarin but otherwise the language provision is unrivaled.
Yes, JAGS is not a destination school but I would hardly see City as such. City draws from a wider catchment, true, but only due to its geographical position rather than "destination" status. Neither JAGS can be considered a "good local independent" similar to SHHS. In our neck of the woods, good local independents would be the high schools - WHS, PHS, Sutton, Surbiton, Sydenham, Streatham and Clapham, etc depending on where you are.
I think among girls' schools in London, only SPGS can boast being a destination school. I think the probability of people choosing SPGS over any other school in London (incl. City and NLCS) is 95% or so.
For boys, there are more "destination" schools, i.e. SPS, Westminster, KCS.
We are actually agonizing over JAGS vs Alleyn's and are leaning towards the latter due to co-ed aspect, but I know that if I were choosing between CLSG and JAGS it would be a much easier choice, especially if commute were a consideration.