There are interesting theories about it tho. Studies around how women and mens symptoms of heartattacks do indicate that there is a pain tolerance difference in general, one of the reason women usually ignoore the signs.
Just recently there have been similar tests on a microbiology level. 'The manflu' might actually be getting a scientific basis in the same area, women not feeling as bad from the symptoms as men do. Labrat tests have been done and the rats given estrogen do get more alert when infected with the cold virus than the ones without. https://www.bmj.com/content/359/bmj.j5560.long
This is pretty much where we are with that line of study tho. Still inconclusive but it does indicate that estrogen does dampen pain in general, on both a sickness symptoms and physical pain level.
Tldr: we can't know wich is worse, ever, men handle pain worse 'in general', so it is most likely childbirth though.