If you measure responsibilities by number of missvot the answer is clear. Otherwise, while it may be nice to know, Baruch Hashem both men and women have plenty of responsibilities to keep them both occupied constantly. Usually we don’t count our rights in Judaism.
I once heard from Rabbi Akiva Tatz that marriage is not a division of responsibilities, it is two people coming together to do everything they can to help the other. Definitely something to strive for.