Ahh, the age old question. Men and women have been battling this one one for reasons that are not entirely clear, and we still can't seem to come to a definitive answer.
This is largely to do with the fact that pain is a subjective experience, and no two people will feel it the same. However, as this is a "would you rather", it means that there is one individual (that's you) and one pain threshold involved here.
Pain is caused by the stimulation of nociceptors in response to damage or potential damage. Testicles are covered in these nociceptors because taking a blow to the knackers is likely to cause the kind of damage that is an evolutionary no-no: Infertility. Because of this, men have evolved to avoid ball bashing at all costs by developing extreme sensitivity to pain.
Testicles are also directly attached to the stomach and, subsequently, the vomit centres of the brain via the vagus nerve, and this is what causes the dull ache in the abdomen and the urge to be sick. This makes ball-kicking a visceral, full-body experience as opposed to the more localised pain of getting kicked in the leg, for example.
The muscular cramps and visceral distention associated with giving birth actually produces a similar effect in a labouring woman's body. In addition, there is all of the stretching and tearing associated with pushing a human head out of a vagina. At the moment, we could generously call this a tie. However, we have the issues of frequency and duration to contend with.
The common argument is that being kicked in the nuts is a more frequent occurrence, whereas childbirth happens but a few times. If we're going down this route, let's run the numbers:
We shall assume that the average labour lasts for 8-10 hours, and the average amount of "down time" from being kicked in the testicles (including the initial pain and following nausea) is around 20 minutes, and the average number of children for most women in the West is two. This would mean that a bloke would have to be fully kicked in the nuts (not just clipped) between 48 and 60 times in a lifetime to match up. Now, without wanting to sound too judgemental, if you're getting kicked in the nuts 60 times, you might want to consider improving your social skills.
Verdict: Get Kicked In The Nuts, Obviously.
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