To be really honest, I feel that there is no “best” school, but only the school that is most suitable for you. The fact that Deerfield saw sth in you that they felt would be a good fit in them and that Andover didn’t, suggests that maybe you are more suited for Deerfield.
These AOs have done these things for years and they know it when they see a kid that will do well in their school. After all, that is what the whole admission process is about.
My suggestion is that you go with Deerfield (or Milton). Love the school that loves you.