The linked question, Do women prefer men with a sense of humor? along with the Stanford university study linked in the question show evidence of differences in how humor is processed and that humor likely evolved as a sexual selection trait.
If that is the case it would make sense that men would tend to be funnier than women. Men would be actively competing to be funnier than each other, which would not be as true for women.
As to whether or not men are objectively funnier than women, this New York Times article about a study at the University of California, San Diego which measured the perceived of how funny each gender was in a blind test.
A selected excerpt:
How to determine something so subjective as what makes one person
giggle and another give a dismissive shrug? To create a blind test, 32
undergraduate men and women were asked to perform a variation on the
New Yorker cartoon caption contest. Each was instructed to be as funny
as possible coming up with 20 captions for 20 cartoons in — think fast
— 45 minutes. The researchers then asked 34 undergraduate men and 47
undergraduate women to rate the funnier captions in pairs, without
knowing the sex of the authors, assigning scores to the writers
depending on how they fared.
While men were deemed ever so slightly funnier (0.11 points out of a
theoretical possible score of 5.0), they were mostly considered
funnier by other men. There goes the peacock theory. Other
differences? Men tended to use profanity and sexual humor slightly
more often than women (only slightly, thank you, Melissa McCarthy),
though neither sex necessarily considered those types of jokes
A link to the study.
I find it odd that blind as opposed to double-blind tests were performed, as this is a subject area rife with bias.
Even so, the findings of at least one study show that men perceive themselves and other men to be funnier than they are and that men are considered funnier than women, although only marginally.
It's hard to say anything for sure at this stage beyond speculation, as only a single study has been performed.