In my experience, the "top tier of kids" is more cultural than school-specific. Even in schools like TJHST there's usually 10–30 students in the school that really care about achieving, while the other 90% don't put in much effort (beyond your typical public schooler). There are a few feeder (public) schools on the coasts, but most of the private schools differentiate by extracurriculars (fencing, rowing, horseback riding) rather than academic excellence.