I hope some input from the other side is okay here.
I want to momentarily propose the idea of this question asked the other way, as I think that might be more interesting. The reason I say it might be more interesting is due to the results from surveys that Riot has collected from League of Legends. In case it adds context for those unfamiliar with the game, the characters in the game are predefined champions with their own lore, gender, abilities, and so on; you don't create your own. With that stated, apparently it goes like this...
Guy players are pretty split on playing guy and girl characters in the game.
Girl players, however, are predominantly playing girl characters. And by "predominantly", it's apparently to the extent of "almost only play as girls".
I'm not sure how Riot gathered the information; maybe they took the surveys people can opt-into (which typically does have a gender question going off of memory the one time I took it forever ago) and then looked at the champion play history of those accounts answering it. That's definitely limited in application since it's one source and it applies to just that one particular game, but I found that interesting all the same.
As for myself, while I tend to play as girls when given the choice, I also have very little trouble playing as a guy and relating to the game and story from their eyes. And like, it depends too. If I'm playing something like The Sims for example, then "I" might be a girl for, but that doesn't mean I'm actively avoiding making or playing guys entirely, and at times, I might even guide one primarily for a while. If I'm playing a game with a predefined characters instead (which I typically prefer much more than creating characters, by the way), then I'll generally have no issue seeing the game through their eyes.
It's funny because I never really put much thought into this. Yes, a girl character is more natural for me in a game and I'll almost always choose one in games where you're creating a blank slate, but most games I play have predefined characters. I guess I don't look just at gender but instead at personality more. For example, a game like Life is Strange has Max and Chloe, right? Both are girls, but I'd "relate" to each of them very, very differently. So gender isn't the first thing that enters into my mind, at least not consciously.
But glancing over this thread, it seems guys do in fact approach this from a different angle, as I'm seeing many just say they prefer a split for variety sake, or because a girl character looks better, haha. Which... I guess I actually can relate to a bit despite saying it was different for me, as I don't mind guy characters sometimes for that reason, but the most important thing isn't that. Most important thing is that I'm just wanting to get invested into their plight or their story or what they're going through, regardless of if they are a guy or a girl, and sometimes a guy character makes certain personalities more believable whereas on a girl character it might feel a little forced.