I've seen this debate come up every now and then (maybe you haven't, but I've been in it more than once), and it's always dividing between guys who have certainly been hit in the balls before (myself included) and girls (and their whipped boyfriends). So I want to say here why I believe getting hit in the nuts is worse, but feel free to vote and add your own input.
To me, it's purely a matter of context. I can't know the amount of pain childbirth inflicts for obvious reasons (I lack the mechanisms that allow for such an event to occur in me). Conversely, women cannot know what it feels like to be hit in the balls. They can try to imagine it, but they too lack the parts necessary to truly comprehend it. Thusly, a discussion on which one "hurts more" is pointless because each side can't know what the other one is talking about.
So, all we have left is context. Now, in an average childbirth there are several factors to consider:
Childbirth
1. Most pregnancies are expected, or at the very least take long enough to start showing signs that the side-effects and most certainly the delivery are never a surprise.
2. Most deliveries are well prepared for and take place in a hospital or some facility with medical equipment and personnel on hand.
3. If the woman isn't dumb enough to want it done "natural," she'll generally be loaded with painkillers, which I'm not saying would render the birth anywhere near painless, but would at least reduce it some amount.
4. Childbirth has rewards. Namely, a child! And what better gift can there be?
Now, obviously I'm not including the negative aspects of pregnancy and childbirth like the weird side-effects and the pain and the having everyone in the room see your vagina and also see you crap yourself and your new baby. I was just highlighting the good things about an AVERAGE pregnancy (unconventional circumstances are, well, unconventional).
Contrast this to getting hit in the huevos, which has absolutely no positives and a long list of negatives. It's almost always by surprise, it can do long-term damage, it's incredibly painful, it's humiliating, it's a highly exploitable weakness, and it's repeatable at an interval FAR shorter than 9 months. So if we exclude the meaningless point of which hurts more, I feel safe saying that in the debate over the gender-specific agonies, wanging your walnuts is far more unpleasant and far less rewarding.
Now, feel free to way in, and also to hurl insults at me over how stupid I am for saying this and whatever.