It is up to you really but, you have to put a lot of things down.
This is our story!
My daughter is now in Year 11. She goes to an independent school. She didn't get a place into a selective grammar school and she wanted to be in a high academic school, so we compromised a lot of things to sent her to a private. She has done well and the fact that all girls have gone through the same selection process (for your case, CITY), it means that although they are put in groups, an average girl means that for GCSE this is grade 7/8.
She applied for 6th form. DAO is possible for her. I would love to sent her to DAO because its 2 more years of fees. Remember each year this is 20k (includes coach).
My thinking is that DAO AL results and her own school results for the subjects she will do at AL are similar. This is why she agrees to move to a school for 6th form. If money was not an issue, I wouldn't bother as she is quite happy at her school and as parents we are also happy. But 2 years of 20k = 40k and she definitely wants to study so at least she can use those 40k for later.
Good for him he can choose a school, I think it's always good to have an option rather than being stuck with a single school choice. Good luck to him and remember wherever you/he thinks he will be happier, that's where he should be.
But, at the end of the day, it's entirely your decision.