In my opinion, there is no comparison. The pain of giving birth is so much easier. In addition, at the end of it, you get your baby. With Crohn's pain, at the end of it, you don't get anything but a little relief. Also, with having a baby, you expect the pain, and you prepare for it, taking classes to learn breathing exercises, best positions and such. And, at least for me, my husband was helping to keep my pain levels low by massaging me and such.
As for contractions vs. Crohn's pain, the contractions are sharp, but not like the Crohn's pain. Think of the worst menstrual cramps. That is what contractions are like.