You cannot compare the Old World and New World as far as native populations. Pre 1492, New York was indeed populated by native peoples. The only non-Americans documented to have reached the Americas before the time of Columbus were the Norse, but they did not survive long and did not have a major impact on native life. So from 15,000 years ago(when humans populated the Americas) until 1492AD, the Americas were populated by the natives and the natives only. The same cannot be said for the Old World, and especially the area in which we are talking about.

The Middle East and surrounding area has been the crossroads long before the time of Christ. Ancient Egypt which existed before the time of Christ, invaded both Nubia and the Levant and took in slaves from those populations, not to mention peoples from the area now called Libya. Mesopotamian princesses married into Egyptian royalty. So, I say again, if Christ existed, in my opinion he looked like Osama bin Laden. However you like to categorize that in terms of your classification of races, then so be it. This also brings up another issue which is that it's very problematic to impose current arbitrary definitions of race/ethnicity on past cultures. I face this problem now when looking at pre-Inca societies in the Andes and identifying ethnic groups. It just isn't possible.