Sexual selection drives faster evolution in males. The X chromosome is potentially an important target for sexual selection, because hemizygosity in males permits accumulation of alleles, causing tradeoffs in fitness between sexes. Hemizygosity of the X could cause fundamentally different modes of inheritance between the sexes, with more additive variation in males and more nonadditive variation in females. Indeed, we find that genetic variation for the transcriptome is primarily additive in males but nonadditive in females. As expected, these differences are more pronounced on the X chromosome than the autosomes, but autosomal loci are also affected, possibly because of X-linked transcription factors. These differences may be of evolutionary significance because additive variation responds quickly to selection, whereas nonadditive genetic variation does not. Thus, hemizygosity of the X may underlie much of the faster male evolution of the transcriptome and potentially other phenotypes. Consistent with this prediction, genes that are additive in males and nonadditive in females are overrepresented among genes responding to selection for increased mating speed.
Why does sexual selection usually occur via males? The typical logic is reproductive skew. That is, one male in many species can produce orders of magnitude more offspring than another male. Such an extreme range of variation is not possible with females across the same range of genetic fitness because of the constraints of female investment in the gamete (sperm are cheap and plentiful compared to eggs). These sorts of situations tend to result in powerful sexual dimorphism as the traits which are selected for males might not be so beneficial for a female. Over time the two sexes shift toward differing optimal morphs. Large, aggressive, risk taking and showy males, as opposed to smaller and risk averse females. So that's the logic for why sexual selection should operate via males, they're the ones where variation in genes can result in incredible variation in reproductive fitness (once a female is inseminated copulating with more males isn't going to increase her reproductive fitness much [though it might increase variation in offspring], but once a male inseminates he can "sow" other fields).
But the paper above makes a different point: the extant genetic variation of males is more amenable to selection than that in females. Remember, the rate of evolution is proportional to the strength of selection and additive genetic variation. The breeder's equation states: R = h2S, or, response to selection is equality heritability (additive genetic variation) multiplied by selection. If one thinks of selection as working through reproductive skew correlated with genetic variation, then males have more theoretical range to increase or decrease the frequency of an allele in one generation.
Why do males have more additive genetic variation? Males possess one copy of many genes because the Y chromosome tends to be mostly nonfunctional. This is why males exhibit sex-linked traits: a nonfunctional copy inherited from the mother has no complementary copy from the father. In females such an inheritance generally results in the trait being masked, so that she is a heterozygote carrier. This masking means that the allele is shielded from selection, the genetic variation is expressed through dominance, not additivity. If there is a beneficial allele which is recessive it often has a very difficult time increasing in frequency because you need two copies of that variant within an individual to increase the frequency of the allele. If it is a new mutant in a large population it is almost certain to be subject neutral processes and so go extinct (one way around this would be immediate matings between siblings, and successive generations of inbreeding. Or, very small populations which fix rapidly). Now, consider that the mutant is sex-linked, so that it expresses in males. That means its fitness benefit can be brought to the fore immediately, preventing its extinction and allowing it to shift up the frequency curve over time to the point where many females might also be homozygotes and so gain fitness advantage!
So do I believe this? Well, I don't really know. The authors make some points about gene expression and what not implying that this phenomenon is not just localized to the X chromosome. Fair enough. But it isn't like we're all elephant seals, sexual selection is a mild force for many species. And the sex determination system varies, in birds females are heterogametic, but males are still the ones generally subject to sexual selection.
ScienceDaily as an expansive summary. Though using the classic case of the Peacock might not be the best case when we're talking about sexual selection and the heterogametic sex.