I'm not sure about this answer, because it depends on what you actually mean by listener, but here goes: I think men are better listeners. I think women like to talk too much, after all we do have somewhere in the region of 20.000 words to use every single day, that nr. is much, much lower when it comes to men. But then, we can argue if men are really listening and that is another subject altogether. Finally, if you mean really, really listening, well, then I think it's more or less the same, men and women alike.
It is unfair to generalize. There are good and bad listeners from both sexes. I believe that the art of listening while others speak is acquired by a person during growing up years. Once you reach adulthood, it is a difficult nature to develop; either you have it or not.
Can it be categorized by gender? I know good listeners of both sexes. I think it would depend on who they are as people, how they were raised etc. Listening is an art and people have to try and be selfless in that moment to be a good listener.
I am a good listener, I think, but then so is my husband. It depends on what you are talking about at the time. If he is watching TV, I don't bother him because he won't catch hardly anything I say. And, if I am busy writing, I probably will not hear half of what he says to me. Generally, when it is really important, we state the matter needs our full attention and then we talk. Guess it depends upon the person.