This is a great response, and I agree everyone who comes to this forum asking to compare school districts would benefit from reading it.
I would just add, in response to the OP's questions, that wealthy towns like Bronxville can support private foundations to support the schools. Check out the website for the one in Bronxville -
BSF: Home which boasts about bringing technology, arts, science, athletics, drama, foreign language, music, facilities enhancements, etc... to the school system every year (through grants). These additional programs are certainly attractive to parents, and the whole system seems to foster the idea that it's a pseudo-private environment. They solicit funds and updates from alums the way a private school does, and foster loyalty and support with newsletters and reunions. I've met many adult "Broncos" and they sure share a common bond. So, in addition to the fact that parents are driven and drive their kids to succeed in these towns, the wealthier of the towns do provide enhancements to the curriculum and extra-curricular activities that are a meaningful draw. I only picked Bronxville as it was specifically requested - many towns have something similar.
Oh, and I'm realizing that this is an old thread, but hopefully this info is helpful to some!