Hi my daughter has to choose between the 2. I know one is independent with a small batch and the other is a large school. We moved from Hong Kong a few months ago and she was in a IB school in HK. She went to a state school in London for last 3 months of her year 6. She was able to adjust well and was even selected as narrator for her school play. Her strength is language and she is average in Maths. She is not much into sports. She always makes few very thick friends. Sydenham would also mean 1500+ pounds a month.
We are also looking around south london on where to live long term and plan to buy a house so it's possible that next year she may have to change her school. Would be good to know if Kingsdale is worth keeping if we move as far as Putney and she has to travel.