That’s a very interesting question. Yet in most places more would come in play as well such as quality of schools. Even in a public school system there is often a large difference in quality, that often also based on neighborhood and such demographic factors. And, of course, education.
Otherwise the only way to truly effectively measure that would be by isolating the children from any outside (and family) influence in order not to contaminate the outcome.
There are so many factors of course and diet is just one, education another. When it comes to early childhood education however, there is a great deal that the parents can effect just by talking with their kids more, something that is being lost as screens increasingly become babysitters. As I see it though, a parents job is to do the best by their kids given their capacity, even if it is not the best possible. Diet is an easy place to have an effect as essentially most people know what is healthy and what is not.