Women seem to report pain for specific conditions as being more severe on average (and notably go to seek medical attention more often), but these reports are subjective, so they may not be reflective of how women actually experience pain compared to men. Despite this, it seems like the threshold for detecting pain may be apparently lower in women than men on average
[6] [7]. From this, it seems like women may, at least, respond to pain (or feel the need to have it treated) with greater severity than men, if they don't feel it more severely.
This article from a decade ago seems to offer a decent review of sex differences in pain research.