This deserves an analysis far more nuanced than I'm able to deliver. How has the integration of Italians versus Irish gone in New York? I can't answer that, because I've never studied it. I suspect it went better than the integration of whites and blacks in the South. Why? I can't answer that for the same reason.
I suspect we're both right for different reasons under different circumstances, and it would be fascinating to actually go through the histories and anthropologies to understand what those reasons and circumstances might be.