Several articles have recently discussed the issue of whether and why men are funnier than women. Most of these pieces take an evolutionary-psychology approach to the issue, claiming that men need to be funnier—and women need to be receptive to men's humor—as a function of mate selection. Humor is the human-male equivalent of pigeons' puffing out chest and neck feathers while doing a mating dance to attract females. Get a woman to laugh, and you're partway there when it comes to luring her into your horror-cave and eventually turkey-basting her with your warm, slimy DNA.
But are men funnier overall? Some of the articles dispute this assumption; some even outright deny it in favor of the notion that women are the funnier sex. My own intuition is that the jury is out, and that people these days run a little too quickly to evolutionary psychology to explain every little aspect of human behavior. (If evolutionary psychology had that much explanatory power, it ought to have commensurate predictive power, which our law-enforcement agencies would appreciate. Alas, EP does not: it's mostly post hoc analysis, which means you should approach EP with a hermeneutic of suspicion.)
For what it's worth, here's a recent example of a man and a woman—Chris Pratt and Jennifer Lawrence—trying to out-funny each other:
(I suspect that Jennifer Lawrence's "Where do you keep your Oscar?" dig was stolen from Zach Galifianakis, who used the same joke when he interviewed Bruce Willis for his "Between Two Ferns" show. See here. Either that, or "Where do you keep your Oscar?" is a fairly standard Hollywood joke.)