I feel uniquely qualified to answer this, unfortunately, as someone who has given birth naturally several times and passed a kidney stone when I was 20.
The stone was more terrifying because I didn't know what was happening, I had intense pain and was pissing blood, thought I was dying but by the next day felt nothing and when I went to the doctor he said "you passed a stone, it's gone now, drink more water."
I have had migraines more painful than either, but not as urgent feeling as the bladder stone, if that makes sense. They are depressing not terrifying. Childbirth hurts but doesn't feel like either, it's productive and sort of exciting, you are having a baby. So it hurts a lot but without the negative emotions it's easier in a way.
ETA after reading Velma's post - I never had labor for days with mine, 2 (the first and last) were "precipitous" which basically means I only got the worst part of labor and only for about 20 minutes, one I got the ideal, about 4 hours so time to get used to it and gentler start, and one did take over a day but that was because water broke and no labor, had to be induced (with acupuncture!) and an induced labor hurts more so that was the most painful one, but only a couple of hours. So when I say childbirth not as bad I mean not a complicated one.
