The size of public school districts tends to be an advantage when it comes to special ed, IME. A private school isn't going to hire 3 therapists for the one child with autism. Maybe they find someone to come in for a few hours a week at most.

Public school districts can hire full time therapists and send them around to schools as needed. They also have the legal obligations of IEPs and cannot deny services to students without running up against federal law. They tend to have a lot better staff with a lot more training with a lot more hours they can devote to the kids.