Artists' depictions of Christ, as well as the people he ministered to, vary greatly, and correspond to the race/nationality of the artist, as has been stated. Rembrandt painted Christ and his followers as Dutch, even wearing the styles of clothing popular in Rembrandt's own time. Carravagio did the same, and some 19th century American painters did as well. It's not about depicting what anyone actually looked like; it's about depicting a feeling or emotion, and helping the viewer to identify with what's going on.
I've seen certain depictions of Christ as African/Asian/Hispanic, and the ones that are actually effective are the ones that adopt the actual style of that culture. A Christ figure that looks Asian in a modern, realistic style doesn't seem to send its message very well, at least to me. A Christ depicted in the highly stylized traditional Japanese style of painting is much more effective.
I find this similar to depictions of Buddha across Asia; the Indian Buddha looks different from the Chinese Buddha, which looks different from Buddhas in other Asian countries.
Also... while I know this isn't a discussion on art, I just could help myself.