Males and females have biologically inherent powers, typically discussed in terms of the power to generate life, but there are others. It would make sense that there are sex-specific spiritual powers that are inherent as well. And there are by far many other, general types of power that members of both sexes can cultivate irrespective of biology or spiritual makeup.
The strongest theme in this thread seems to be the challenge of understanding why the Aaronic and Melchizedek Priesthoods are conferred only upon males; why another “order of the priesthood [meaning the new and everlasting covenant of marriage]” is entered into by a man while the covenant relating to “this order of the priesthood” requires a woman (D&C 131:2), and why this yields the highest blessing mentioned in scripture, the Church of the Firstborn.
From the man’s perspective, the first order is bestowed upon him (with a covenant), the second order he enters into (with a covenant), and the third order he “communes with” in fulfillment of the covenant. The first order requires the man to be called and receive the order; the second for him to seek and enter the order, the third to be chosen into the order through his righteousness. The woman only has to be chosen into the last order, through her righteousness.
Why this difference? If it is because women are more spiritual, it may be that they have, in this particular aspect of pre-mortal / spiritual makeup, already developed the fundamental receiving and seeking skills that men must develop by virtue of receiving and entering into orders of priesthood. Adam had to come to earth alone, fall asleep, and wake up again with a companion; Eve came into the earth with an instant companion. Eve, thus coming into the world with this natural affinity (not alone as Adam was) did not possess natural enmity against the serpent, and so without priesthood was able to get things going.