In the combat rules for dark phoenix, It says that she can be pushed every turn but is dealt pushing dameage each time, but she has power cosmic wich cancels pushing damage.

my question is witch rule takes priority. I beleive that If it is in the phoenix rulebook, she should take the damage, as her rulebook is specific to her and not a standard big fig rulebook. why would they put that there when she has power cosmic?

Because if the Power Cosmic TA is canceled (either by the player or via the Disbanded BFC), Dark Phoenix will take push damage just like the Sentinel or Sinestro.

Unless YOU turn the Power Cosmic TA ability off, she will not take damage for pushing, i.e. she can take an action every turn without taking pushing damage. I believe this was clarified in a FAQ.