Well I think it depends, and keep in mind I don't know the type of people your parents are so ultimately read into this what you will. Your mom is saying go with her, well, that isn't a particularly altruistic perspective. She is being very blatant about the fact that she wants you to pick her over your father.
Whereas your dad, you haven't really given his perspective on the matter. Did he say "Go be with your mom", or perhaps "It doesn't matter who you choose, as long as your happy"? Etc, etc. My personal feelings on the matter is that your mom is pressuring you into abandoning your father for her on your birthday. I tend to automatically side with the parent who isn't doing the pressuring.
Of course then one has to wonder why she would pressure you to begin with. It could be simple resentment towards her ex-husband, her trying to play favorites. Though since we don't know much about your relationship with either parent that could just be her showing that she cares. She might be the overly emotional sort in that regard. Your dad however could, for all we know, be the much more reserved type who tends to just be of the opinion "Do what you want, I don't really mind or care either way".
Then it also depends on who you would personally rather spend time with. You presumably love both your parents, but its not uncommon to have more in common with one than the other. We don't have a full view of your home life here, so again for all we know choosing one parent over the other is going to lead to that rejected individual pulling away emotionally or punishing you. I would truly hope that your parents are bigger people than that, and I suspect they are, but if that is a consideration you should weigh it as well.
You have to make a particularly difficult decision, and if I may make a suggestion, ideally if your parents can stand to be in the same room with each other, why not spend it with them together? Even if they can't, it would be unfair for you to suffer simply because they find it difficult to say civil for two hours.