My kids actually went both to a top (probably the top) private school in our area and to a top public school. They could write you a book about the differences, but one of them wasn’t where they went to college. The kids at the public school who were most like the kids at the private school, in terms of demographics and attitude – and there were a number of them – went to the same colleges. My older child, who changed schools in 11th grade, pretty much knew where the GCs at the private school thought she should end up and, guess what?, that’s where she went to college. (Along with five other kids out of the 24 who had been in her 4th grade classroom, believe it or not. At a college 700 miles away. There may not be any feeders anymore, but if so that’s a recent phenomenon.)
In terms of academic ability, the top kids in both schools were interchangeable. A kid who would not have been among the top 4 or 5 kids at the private school wasn’t going to be among the top 4 or 5 kids at the public school, either, although everyone at the private school would have been comfortably in the top half of the class at the public school, and most of them in the top quartile. (The public school, being somewhat rigidly tracked, without ever acknowledging it, the kids in the top quartile of its class didn’t spend much class time with poorer students, so that the academic experience was very comparable). The public school kids were much more STEM focused, and more exclusively STEM focused. They were much more diverse, in every way: race, religion, national origin, class, politics. The public school was overtly competitive (although the kids did not undermine each other at all); at the private school overt competition was declasse but covert competition was rampant. The private school was warm, family-like. It had exquisitely personal college counseling, part of the point of which was to nudge equivalent students to apply to different colleges so they weren’t competing head to head. The public school was a complex structure of interlocking cliques, each of which was tight and warm, too, and usually had some star faculty member at its core; its college counseling for top students, however, mostly consisted of students passing folklore back and forth among themselves.