I have two daughters, and it seems like a lot of people are compelled to point out to me that:
1) Boys are always closer to their mothers
2) Girls are always closer to their fathers
I guess they're trying to tell me I should have had sons? That I blew it?
Aside from the fact that it's obnoxious to say that to a woman who has two daughters, I think it's untrue. Correction: I know it's untrue.
I love my father and I consider myself close to him, but I'm far closer to my mother. When I was growing up, it was my mother who heard about every single one of my friends, all my crushes, my dates, etc. My father only knew who I was friends with or dating on a strictly need-to-know basis. In college, I talked to my dad once a week on Sundays, and my mother every single night. I can't even imagine talking to a man (even if that man is my father) about some of the personal things I talk to my mother about.
I do think girls tend to be closer to their parents in general. I always use the example of a pair of siblings I knew in college: a boy and a girl. The boy used to call his parents once a week, the girl every night. Same parents, same family.
Ultimately, I think it depends on the parents and the child what their relationship is going to be. Your relationship is what you make of it. I certainly don't think it's fair to say that just because my child is a girl, I'll never be as close to her as if she were a boy.