It may depend on the neighborhood of Brooklyn you are referring to, but I don't think most private schools in Brooklyn are Jewish. Obviously, the biggest difference between public and private is that private schools in the area cost a whopping $27,000-$30,000 per year (Packer, Berkeley Carroll, St. Ann's, Poly Prep). With that comes more resources (both in the form of physical supplies and in parental resources and talents), better access to a well-rounded arts curriculum, smaller teacher:student ratio, teachers and curriculum that are not restricted by the confines of constant state testing. Because all private schools are a self-selected group, there will be a "dominant" culture (not in regards to ethnic or race), but a certain intellectual. academic and social culture that children of higher educated parents are exposed to. A home and school culture that values books and reading, valuing the process as much as the product (pressurized state testing that focuses so much on results sometimes warps that part of the culture in public schools), etc. Of course, this is not to say public schools don't have families like this, it's just present in a larger concentration in private schools.