Men's vs. Women's
As of right now, only women's rugby is an NCAA-affiliated sport (source). Sorry, gents. Title IX requires that colleges provide a certain number of women's sporting programs, and having women's rugby be officially endorsed by the NCAA is a low-cost way to help meet that number (source).
Cynical? Yes, but that's the truth of the matter.
Aside from who gets the NCAA's backing, though, there's very little difference between men's and women's rugby. Everyone trains the same, plays on the same size field for the same amount of time, and gets to tackle the snot out of their opponents (source).
In fact, rugby is the only women's contact sport endorsed by the NCAA (source). Ladies, if you want to get into a really good dust-up without worrying about getting kicked out of school, this is your sport.
The men's teams are slightly larger than the women's (source), and the women generally get $1,000 more scholarship money in Div-I and Div-II programs (source).
But in the end, men and woman alike are all in the same teeny, tiny, chronically underappreciated boat.