My take on this is that high achieving students from public schools are academically better, they will do well in their chosen professional fields, but not necessarily be good in business or politics.
Whereas private schools might train them better in leadership and expose them more to the business environments.
Lindsey Fox, the Transport King in Australia once said, out of the top 100 richest people in Australia, he was sure not many had got over 70 marks in their HSC exams.