In the whole sense of the subject white privilege is much more damaging than male privilege.A black person can be male and still suffer from white privilege.At times men may realize that they have a sort of privilege but whites may go on and on without any such realization of it.
I've asked many white women a couple of questions. I first asked them if they believed men have an unearned privilege in America. The affirmative answer came quickly. Then I asked them if they knew any men who recognized that they are privileged. Again, soon there-after came the answer, "no, I don't know any."
Then I ask them if they had white privilege. Most took their time to answer this one. Of the small percentage who acknowledged their privilege, pawned it off on their ancestry's long(er) participation in this economy. Most others denied any privilege present today - maybe in the past, but not presently!
I then point out to them that just as white men can't see their male privilege (whether consciously or subconsciously) you as a white person are blind to your own privilege.
I think that both "perks" are damaging because it is a false sense of superiority. The old adage "you don't get something for nothing" is true. This, along with racism, nationalism, conservatism and classism is just another diversionary divide and conquer tactic to take our eyes off the ball while the rich and powerful gain more wealth and power.