That's a good question.
We do not have enough systematic evidence on that. We can look at complaints, and men's complaints amount to perhaps one-third of complaints that women make—at least at the federal level. For example, in the U.S. in systematic surveys we find that about half of men report experiencing these kinds of behaviours, but only a fraction of those are found to be harassing or threatening. So I would put theirs on the order of 10%, if that of women being harassed is around 50%. So it's a fraction, but it is a significant fraction and proportion of men.
One thing I'd like to point out is the training of people. I teach MBA students—they're mostly men—and when I talk about the harassment of men, they get it, they understand it. Everybody has experienced these gender-based put-downs as men, and that helps train them to see it much more clearly from the woman's perspective.