Actually it depends on which context you mean by “stronger”. If you mean larger, heavier, and hence able to do more brute beating the crap out of each other, I would give you that males have a tendency toward domination there.
However, in terms of sheer physical and psychological toughness, women cope much better at changing environments and stress than men do. The average woman, when death through childbirth mortality is taken out of the picture, lives maybe ten years longer than men. So, obviously one would think that that would be a sign of strength, no? Or maybe just resiliency?
Anyway, genes get passed down because the people who have them have lots of sex and hence reproduce more, not because there is anything innately useful or superior or helpful about them? So, culture and genetics can interact, hence if a culture overwhelmingly favors women with brown eyes over women with blue eyes, then it is very likely that women with the Brown Eyes gene will have an evolutionary advantage.
Brain size, coincidentally, has grown in just such a way. Humans and their ancestors long ago lost the direct advantage given to them by increasing brain size, there was a point at which in terms of interaction with environment the advantage for continued growth became almost nill.
However, paleonathropologists believe, social competition and interaction with peers caused higher brain size to be valued by partners in terms of social hierarchy. Hence, brain size was not valuable in and of itself but simply as a sign of social dominance.
At least that’s one theory.
The real question you should be asking, MasterChief, is not what makes “beauty” good genes?
But instead, why does society have the definition and value system it does of beauty, and what can this tell us about its relationship with the environment and biology?
For instance, traditionally women with wide hips were valued because they could bear more children.
Women with large breasts, mammary glands, could nourish children more easily.
However, conceptions of beauty have changed radically over time. I.E. in preindustrial societies only wealthy people could be fat so fatness was seen as a sign of beauty, whereas in today’s society it is very cheap to be fat, and very expensive to hire a personal trainer, stay in touch with the latest health diet trends, and buy only quality organic foods, hence, now thinness is seen as a sign of beauty.
The same theme applies to a tan. In preindustrial societies, most people worked in agriculture, out in the sun, hence, to be tanned meant that you were a poor agricultural worker, whereas to be pale meant that you could afford to spend your entire day inside, i.e. outside of the area of economic production. So paleness was seen as beautiful.
In contrast, in today’s society most work is done inside factories where there is very little sun and most workers do not get tanned and stay pale. The wealthy, however, can afford the luxery of sunbathing and going to the beach routinely as well as the salon, so tans are valued and seen as beautiful.
In both these cases, it is obvious that it is not the qualities in and of themselves that make somebody beautiful, but the fact that these qualities act as signifiers, symbolizing elite status and wealth, and hence economic security, and greater chances for the survival of offspring.
Sorry if this was too off topic, but it is an interesting question.