If it is any help our DD is joining King's this Sept from a highly academic all-girls school for the 6th Form. She turned down some academically stellar schools for Kings because she wants to be in more rounded environment. She, like your child, is an all-rounder: very academic but loves her sport and music too. And KIng's caters for all that without the 'macho' sports emphasis that you get at a place like Wellington or dare I say it Millfield.
Our take on King's (and believe me we have visited most of the top 'name' alternatives): atmospherics are fantastic; every child we met there was cheerful & happy (not the case at others); staff were vibrant mix of younger staff and old faithfuls (interesting to note high proportion of ex-pupils as teachers); the support staff to a man/woman were cheerful and happy; facilities are great but then that's a given; academically it is strong across the board but not a driven hothouse (still I would say academically a cut above Millfield). it is not as socially smart as Wellington, Marlborough or Charterhouse but that suits us fine, the day pupil element makes for an interesting mix and keeps it socially quite grounded.
We are happy to send DD there as we think Kings is on a roll and she have a fantastic time......so to sum up the case for moving: great head, academics improving, school full, it's starting to get noticed among the chattering classes, ambitious development plans (your DD would reap benefit from) and still relatively unspoilt socially.....
Academically KIng's is pretty strong (20 to Oxbridge last year) so I would say that the preparation for top set kids is probably pretty comprehensive.....and the range of subjects offered is outstanding, so your DD would I would have thought benefit from that attention. The thing to think about is whether you think that your DD's cohort at Millfield will be sufficiently challenging for her going forward.
Hope that helps. Wasnt meant to be an advertorial for King's but we were bowled over by it.