@aidan,
Given the short time period involved, it might be a bit misleading to say the "Y" chromosome has "evolved" disproportionately, and it might be more accurate to say that it has accumulated more variation over time. It's unclear how much natural selection has altered the range of diversity.
As FM says, the result should ultimately be greater sexual dimorphism. As far as "what will result" is anyone's guess, but we might be able to anticipate by asking "what selection factors are (and have been) imposed on human males which alter their ability to produce children"?
For example, selection by women might lead to an increase or decrease in particular traits, although I'm not sure what that would be. Also, the likelihood of survival to a reproductive age would be a selective factor. Also, the probability of keeping your own children alive to a reproductive age would be a factor.
Also remember that "goodness" or "badness" of a male isn't a factor to evolution (unless it alters selection), all that matters is how many viably reproductive offspring he can generate. I've read that Ghengis Kahn was pretty good at getting his genetic code out there, even though his methods would not be approved of by modern society (or even society in his time).