I feel like a lot of humor exhibition is role-based. For example, if someone is in a position where they need to manage an environment, or if they are feeling like they need to be taken seriously, then they're going to focus on creating more structure. If they're not the person in charge or feel more comfortable in the role, then they are usually more flexible and can give their humor sense more free reign.
I guess the roles of men and women could be discussed in various settings (like a marriage, a family with children, a work place environment) to see how this can often play out. Like, are men granted social power in groups more easily than women are, and in what contexts? Or in a family situation, who is expected to provide stability and who is expected to be fun or just assumes the role of "fun one"?
I do know when I've been in positions of leadership, sometimes I find things hilariously funny but have to offer a low-key response in order to maintain stability / just ensure things stay of track. Behind the scenes, I actually push the humor level, which has surprised people at times if they have only experienced me in one setting.
It's really hard to draw HUGE observations about men and women and humor, since the population is so huge and you will always find a variety of people in your day to day who don't follow the collective norm. I guess I find more "combative" humor among men -- get them in a group and they're liable to fall into a series of "one-up's" and smack talking, casually, and find it a lot of fun. Women seem to use humor to stress experiences they've shared. Yes, women can smack talk each other but it's usually over something serious to stake out turf and not just for fun. My ESFP friend (male) laughs at a lot of my jokes and says he thinks I'm a strong woman "because i can take [his jokes]." The insinuation is that he is used to women getting more offended to the kinds of jokes he makes. But as I said, you will find exceptions -- we all probably know a woman who likes hanging out with guys and they see her as "one of the guys" and I bet her humor style fits better in with how men joke with each other, and the same goes for the guy who like spending time with women and finds their angle more comfortable.
I do remember that studies of dating profiles on social media seemed to suggest that men look for women who laugh at their jokes (and view them as having a sense of humor if they do laugh a lot), while women valued a sense of humor in their male partners. (I'm kind of curious how same-sex relationships work all that out, I don't remember seeing studies of that.) I have also found myself laughing at the jokes of people I'm attracted to, as a sign of interest, and tend to make jokes just around people I'm good friends with of either gender.