I am a returned expat from Asia and have done the rounds of the Boarding Schools with several families moving from International Schools, both Chinese and Brit expats, though at 11 rather than 16. CLC seems most often to tick the boxes, especially for International School teachers, and I have been UK Guardian to a few pupils there who have thrived and done well. They have taken a great deal of care to develop strategies for integrating international and home students. Vicky Tuck, the last Head, made a point of really tapping the brains and experience of International School teachers. They therefore tread the line between sensitivity to and valuing different cultures without allowing pupils to form country cliques or use their culture to excuse bad behaviour. It is also a very grounded school whilst being academic. It functions like an academic day school with Boarding Houses as homes they walk back to in the real world.
All of these schools have excellent provision for sport and creative arts.
With the possible exception of Roedean, who do seem to have a similar approach to CLC, I found there was a slight tendency for other schools to treat their overseas pupils as the exotic "other", and allow them to stick with each other and their own language, particularly difficult for overseas pupils who have been in International Schools and may not even speak their own language well. Wycombe Abbey in particular seemed to just want to send one of my DDs friends off with a native speaking group when she didn't actually understand a word!! In some cases it felt that Asian pupils were mostly valued for their results.
Roedean is a lovely school but that clifftop building is forbidding and it doesn't seem as tight a ship as CLC either academically or in terms of ethos. A feeling that it hasn't quite redefined itself having ceased to be the jolly hockey sticks destination of upper class gals IYSWIM.
Benenden is very English, felt like somewhere you tuck away your Princess from the cruel hard world. Downe also very English.
However there really is no substitute for going, visiting and getting your own feel for the schools. IME girls just know when they are in the right place for them. I hope that helps