I've been gaming almost 26 years now (boy, fetch my walker...), in the mid-west and on the west coast, and I've seen three things:
1: Women usually (but not always) play better men than men play women.
2: The number of men who play women well has been increasing, but has not hit parity.
3: The subtlety of cross-gender characters seems to vary with the age of the individual gamer and their generation (how long they've been gaming).
Two things spring to mind that might explain this: The evolution of SF/Fantasy literature over the last 40 years and Standpoint Theory. Second things first:
Standpoint Theory is a feminist theory that says, very basically, that people lower on the social status ladder have a fuller understanding of people in general and social relationships than those higher on the ladder. This is because those lower on the ladder tend to be dependent on the good will (either for support or to avoid abuse) of those higher. Therefore, the lower-downs get better at reading the higher-ups, and the higher-ups don't have to understand things so well because their position of relative power protects them from any negative consequences of their own ignorance.
Historically (and to a depressing extent still today) being male puts you up the ladder (unless you seem to be gay). So, to start bringing this back to topic, women (to generalize) tend to have a fuller understanding of male behavior than most (mainstream) men do of women.
Now, experience with the other gender will mitigate this, so guys with lots of female friends (to whom they actually listen) are less affected than guys who mostly hang out with other guys. And there's no rule that says individual women can't be obtuse about men.
The capabilities of specific individual players may, then, not seem to match the predictions of Standpoint, but it has been my experience that, overall, it holds true.
Now, about the literature:
Gamers who started back in the 1970s and early 1980s learned the genre tropes and character archetypes of the kinds of stories our games tell from reading SF and Fantasy literature. Gaming just hadn't been around long enough to have its own stereotypes yet. The books we read were written between the 1920s and the 1970s, often collections of short stories from the old pulps and the few magazines that carried the tradition into the era of the baby boomers. We're talking authors like Robert E. Howard, H.P. Lovecraft, E.E. "Doc" Smith, Asimov, Bradbury, Heinlein, Fritz Lieber, DeCamp and Pratt, Michael Moorcock, and (we cannot forget) Tolkien. Most of them were men. There were Ursula LeGuin, Andre Norton, Tanith Lee, and Marion Zimmer Bradley, yes, but they were very much a minority.
Now, let's be honest. Even though much of this was a lot of fun, a lot of these writers didn't handle female characters very well, when they handled them at all. The she-devil slut, ice queen, and damsel in distress were about the limit of the range of female characters in the pulps, and these limitations stayed with them into later generations of writers, only sometimes as conscious play with old tropes. Often, the assumption of editors and publishers was that their books were only read by teenage boys who didn't care how true-to-life the female characters were.
Of course there are exceptions. But the fact that those characters stand out supports my point… If strong, realistic female characters were more common, the exceptions wouldn’t stand out!
So, when the players of the early role-playing games (who were mostly male) started simulating their favorite stories in their games, they imported the same character tropes… Including the bad stereotypes of female characters.
It was these players, who went on to write the games of the late 1980s and 1990s, who created the stereotypical characters and situations that are part of gamer culture today. Because they based their modules and settings on the books they read in the early days of gaming, those types became the examples upon which the next generation of gamers based their concepts of play.
Now, in the 1980s and 1990s, more and more female authors made it big in SF and Fantasy. Laurel Hamilton, Mercedes Lackey, Diana Paxson, and Anne Rice all rose to prominence in this era, bringing with them female characters who did not fit the stereotypes of previous eras, often as a direct response to those stereotypes.
Which brings us to White Wolf Game Studios. Their goal for Vampire and the games that followed was to tap segments of the SF/Fantasy fan community who weren’t already gamers, by marketing games designed to appeal to the readers of Anne Rice and other new authors of the same era. This brought in (by design) a whole new set of assumptions about characters and gender, and what kind of situations comprise adventure.
Players of the older games found the World of Darkness, and adopted some of the concepts they found there. Players who started in the WoD moved on to other, more traditional games, and brought their assumptions about character with them. The effect of this cross-pollination was to broaden the stable of stock characters (both male and female) in the collective awareness of gamers.
What this means, then, is that the concurrent rise of women writing SF and Fantasy and the rise of RPGs written with female players in mind changed the way that gamers thought about and played female characters. So players who learned to game since the 1990s, and older players who allowed themselves to be influenced by the games and fiction of that era, had better examples of female characters to go by when they cross-dressed at the gaming table.
For a more thorough look at the evolution of the literature and how it affected fantasy gaming, I direct the reader to Ron Edwards’ Sorcerer and Sword. Michael Moorcock’s Wizardry and Wild Romance also examines the fiction side of this, with only minimal reference to gaming.
Readers interested in Standpoint Theory should investigate the works of Dorothy Smith, Nancy Hartsock, and Patricia Hill Colins.