I don't know how accurate this is, but recent statistics show that far more men self-report as single compared to women in the US, by as much as tens of percentage points if I recall.
It looks like the answer is "it depends." Particularly, on how categories are compared.
There does seem to be a big gap with young people, but overall, the gap is four percentage points. The gap is also much bigger among LGB men vs LBG women which as an aside is interesting in and of itself.
