Engels clearly sees the gender divide as the first class divide and the prototype for all later classism. This is where we get Marxist-feminism originally. From an earlier analysis of Celtic culture, he saw the initial ownership of land as having been restricted to women. As a continuation of hunter-gathering culture, after agriculture, men owned cattle, which needed to continually move, so as not to overgraze land, and women owned houses, which controlled access to safe fields. As agriculture intensified, it was more necessary to hold land, and it was held by women.
The original Welsh tradition of passing land titles to sisters'-son's (maternal nephews), and not biological heirs, is the oldest recorded form of male-to-male inheritance. So women were the holders of lineage, and the ruling class. Then, as war became a larger and larger scale of endeavor, men formed a sort of protection racket that eroded women's hold on land, in what then becomes the prototype of the first economic revolution.
(Sources "We are All Part of One Another" by Barbra Deming, and "Truth or Dare" by Starhawk.)
I don't agree, or at least, if there is such a divide it has more than two classes. A more basic arrangement of human culture from a more modern perspective is the sort of polygynous collective agriculture still practiced in parts of Africa. In such an arrangement, men who hold land have multiple wives, and the remaining majority of men and minority of women are consigned to the role of workers on other's land.
This is supported by evidence that several times more neolithic women than men have descendents. http://io9.com/how-female-dna-came-to-dominate-the-human-gene-pool-1638621568
It is a majority of men and a minority of women because if married men all take two or three wives, then there are between equally many and twice as many men who never get married, while almost all women will become wives. If married men do not take two or three wives in this model, they cannot feed their cattle in hostile seasons, because there is a hard division of labor: men do not farm, they only clear land and manage animals. Tropical land where we originated in Africa is often single-use, once you grow on it one season, you have to let it grow over before it will bear decently again. So clearing land is a constant occupation that used up the labor of all those unmarried men.
In such a system, one cannot make the argument that men as a whole or women as a whole are the more powerful economic class, since the majority of men hold nothing, and the majority of women jointly hold land, even if they cannot hold land in their own right. Men in such societies also do not hold land until married. The inheritor is the son first chosen by a woman's family for an arranged marriage.
Eventually two things happened to break this down. We developed a more plant-based diet, so the women's work became much more important than the men's, and the men started doing it with them. And we learned that we can improve soil by putting waste back into it, so land recovers fast enough that it does not have to be cleared of trees each time. I don't imagine it took too much pressure to break down universal polygyny once that was possible -- humans do not seem predisposed to sharing mates well.
From such a direction, you can only see this as a class system if you see it as a three-tiered one where women form the middle class and men form both the upper and the lower class. But that keeps gender itself from being a class divide per se.
To my mind, this accords better with reality than the Marxist-Feminist notion that since that first deposition from power women have always been the losers. In modern society we have difficulty with women leading, but 90% of the people we kill, lock up or just let die are male. The fate of women is thus intermediate between the fates of these two classes of men.