Yes, those particular differences are what you would expect to see given the different selection pressures that operate on male and female humans. As my previous link explains:

In many non-monogamous species, the benefit to a male's reproductive fitness of mating with multiple females is large, whereas the benefit to a female's reproductive fitness of mating with multiple males is small or non-existent. In these species, there is a selection pressure for whatever traits enable a male to have more matings. The male may therefore come to have different traits from the female.

and later:

Some biologists theorise that a species' degree of sexual dimorphism is inversely related to the degree of paternal investment in parenting. Species with the highest sexual dimorphism, such as the pheasant, tend to be those species in which the care and raising of offspring is done only by the mother, with no involvement of the father (low degree of paternal investment).

...

According to Daly and Wilson, "The sexes differ more in human beings than in monogamous mammals, but much less than in extremely polygamous mammals."

The differing parental investment between males and females together with the differing ease of confirming parentage both tend to encourage a mating preference in males for quantity and a mating preference in females for quality.

The precise degree to which this holds in humans is obviously an empirical question. The evidence I have seen leads me to place a high probability on it being more true for humans than is commonly acknowledged. If you want references I can provide some. So to answer your questions: yes, there are strong reasons to expect a difference between genders in this regard and yes, there are strong reasons to expect the particular differences nazgulnarsil suggested.