NYC has an income tax unlike Lakewood. It also has Wall Street and more commercial buildings than Lakewood has residents, which are a big sources of tax revenue.
Also, In Lakewood Frum Jews are in the majority as opposed to NYC. So the ratio of Jewish students to public school students are different, 3 to 4 yeshiva students to 1 public school student in Lakewood. While in NYC it’s about 10 public school students for every private school student.
Also NYC has mass transit which many students both public and private use instead of school busing. NYC has sidewalks, crossing guards and traffic lights at busy intersections unlike Lakewood , this reduces the need for school busing,