I don't think you can go 'wrong' with either of the decisions - both are decent schools and you and your DD obviously liked both enough to apply.
I would go for the one with the easiest independent journey. Neither school has their sport fields close by, so perhaps the location of those might help with the decision (as your DD is going to be involved in all the after-school/weekend sport if she's sporty!).
SHS Juniors has always been academically selective and they used to offer guaranteed senior school places, but think this has stopped recently. In the SW London Indie school stakes, SHS is definitely known as 'less academic' than many others, but in fairness there is little between the top 50 in league tables for 'value-added'.
If worst comes to worst, you can always change after Y7 or for 6th form!
Good luck! I have friends with DDs at both schools and they are very happy with their choice (interestingly, one at KGS used to go to SHS Junior school but wanted co-ed for Senior School). Another, whose DD started at KGS in Y8 had an awful time at her Y7 choice of school and is now finally very happy at KGS. So much depends on the cohort/class mix and that is entirely unpredictable.
If you have a gut feeling, go with it!