Wow, I wasn't expecting to see so many posts when I checked back. Thanks for the insight everyone!
From my experience, it seems like there's no middle ground. Men who do show emotion and sensitivity are coveted by women but looked down upon by their male peers. If a guy shows emotion by crying in public, for example, other men would make fun of him for being a sissy but many women would become intrigued or even fawn over him for being sensitive and unafraid of showing it. Similarly, women who have male characteristics are coveted by men but frowned upon by their female peers. I'm sure a lot of people have heard about how guys always look for the "gamer girls" or the sporty girls who have the same interests as they do.
It's sort of a question of: do you want to be a lady's man who can show sensitivity and intrigue women or a man's man who's a bro and a tough guy? Or for women: Do you want to be a tomboy who fits in the with the guys so they can be comfortable around you or a girly girl who men admire but can't always relate to?
I guess it just depends on what set of social pressures come along with your gender and whether or not you conform to them depends on the perspective you want to be viewed from.