White privilege: Exists, but anyone who actually brings up white privilege is pretty much blowing it completely out of proportion. As with everything in life, it is far more complex and nuanced but being white in the western world comes with a number of advantages.
Asian privilege: I have never heard of this before, but in the western world, despite the smart Asian stereotype, my understanding is Asians still receive a fair amount of prejudice against them.
Privilege is really contextual. White privilege only really applies in western society. Being a white westerner in Asia is pretty much the equivalent of putting a target marker on your head for "sucker". While an Asian is far more likely to be able to integrate into that society. Being white in Africa will generally provide you with a strange degree of safety and civility, but true trusted integration is pretty close to impossible.
Privilege, its complicated.