pizza,

I think it's a matter of tax base and allocation of city and state resources.

Current residents of new Little Italy are going to be singles or couples with no children.(young professionals, hipsters,gay couples)

Residents of the area of upper Manhattan you mentioned and outer boroughs are going to be old school(in the American sense) families with a lot of children and extended families.

The state is taking more in and spending less in new Little Italy....public school class sizes are probably very low in that area for example.
Average income levels have something to do with the trends that neighborhoods take but I think things such as household size play big factor.