Demographically, Westchester is the least white, with its Hispanic and especially Black populations concentrated in the cities.
Nassau has the most Blacks living in suburban settings I suspect though.
Bergen is the most Asian, due to the very large Korean population. Nassau I believe has the most Indians and Chinese, and I suspect its proximity to Queens means it's likely to grow signficantly. Few Asians in Westchester or northern NY suburbs.
What about Filipinos? I'm guessing they would also be less common in Westchester than Nassau or Bergen, but I'm not very familiar with the Tri-State Area.