on an individual level, it doesn’t matter which citizenship you have. If your profile is not good enough, it doesn’t matter if you have a Mars citizenship.
I agree with baobaobear. Face-to-face communication definitely will give you more chance, at least it works for Canadian schools. I know couple of cases.
It also does make sense. Unless you really stand out, I guess the quality of most applicants is very close. A good impression will help you win this subjective game.