I empathise with daphne, we too had the same problem last year. Needless to say, many people face far worse dilemmas about secondary schools at this time of the year but that doesn't make the choice any easier.
Academically, there's not really all that much difference between the two. Seven years of paying fees will basically turn one A-level from a B to an A*/A, and to balance that your daughter would probably have 11 GCSEs rather than 12 or 13. Although you get classes of 18-20 rather than ~30 in KS3 that difference will diminish once they start GCSEs.
As I've said on the KES/CHB thread, I don't see any difference in the extracurricular provision between KEHS and the grammar schools although I suspect that there might be a little more proactive encouragement to take part at KEHS.
IMHO the choice is down to (a) personal factors specific to your daughter and where you think is best suited to her personality, strengths and weaknesses and (b) if that makes KEHS your first choice, whether you believe you have enough financial security to pay the fees for the next 5/7 years (because if you turn down the GS place now, it's very unlikely that the opportunity will ever present itself again). I'm not going to try and generalise about either aspect, but if you have any questions feel free to PM me.
We chose KEHS in the end, mostly I think because of its light touch and slightly unconventional approach which we think will bring out the best in our daughter. She has absolutely loved it from the first moment and has a wonderful time there. I can't say that she's taken to science, sadly - major reason for us preferring girls schools!
- but she is (for example) enjoying sport for the first time, something I'm sure she wouldn't have done in a larger school. I don't think it's a coincidence that both our AtoZ's daughter and ours are enjoying things that they perhaps wouldn't previously; as well as the teachers' enthusiasm I think it's also due to the school working quite hard on encouraging the pupils to be supportive of each other so they all feel confident about taking part.