Hard to say. I believe that it depends more on the individual. Men and women have different issues and struggles independently of each other, just for being the gender that they are. But I don't think it's as black and white as one or the other. The individuality factor puts that all over the map.
Of the traditional gender roles, the masculine role is more responsibility because it's at the bottom of the stack. If the man fails to protect and provide for his family, then the feminine role becomes rather meaningless.
Of course, outside the traditional gender roles things can be divided any way one sees fit. In an ideal world the division would be equal, but in most relationships that is not the case.