Can we agree at the start that we're talking in stereotypes and generalizations? Everybody's different, so the comments here (including mine) shouldn't be taken as meaning that all men or all women are a certain way. It's more about general tendencies than about specific individuals.
That said, I wonder if a similar thread could be made asking if lesbians appreciate women more than men do. There are lots of differences between the sexes - not just the anatomical ones, but ways of thinking and behaving.
Regardless of sexual orientation, men are men. It's natural that gay men would, in many cases, understand and respond to another man's attitude and behavior in a different and more accepting way than a woman would because the behavior is natural to us, too. Or, if not always natural, at least understandable.
For example, I have observed that many women, even sophisticated and worldly women, really don't get male sexuality. Among other things, they don't understand how men can so easily detach sex and emotion. (And, I'm sure, it could equally be said that many men are clueless about female sexuality.)
So, in that sense, I think gay men often understand straight men better than women do and don't judge them as harshly in some areas.
Also, we are not raised to expect men to support us or take care of us, so our expectations are lower. Modern young women have been brought up in a weird, entitled, and almost schizophrenic way: On the one hand, they expect to be treated as fully equal to men in every sphere of life, and yet there are still many influences that teach them to expect men to treat them as special, put them on pedestals, take care of them, etc. It's no wonder things are a little confused.
I think these two things - greater understanding and lack of expectations - tend to allow us to appreciate men more than women do.
But, again, I think the exact same argument could be made about lesbians and straight women.