Nope, not the same at all. Circumcision involves the body of a child which many here believe neither the mother nor the father have the right to make such a decision whereas childbirth involves only the body of your wife. Regardless of how you may feel about how childbirth should ideally be handled the decisions around your wife's labor and delivery should be ones that she is completely comfortable with no matter your feelings.
As I said before, I'm not trying to make the decision for her. However, my feelings should definitely be taken into account since I am the father and it is also my child. I think discounting the father's feelings because he's not the one having the baby is a bit traditionalist. My reasons and feelings are not unfounded. I've had plenty of time to research things in the best interest of my wife and child. The more education we both have, the more prepared we will be, and the more our child will benefit from it. So yes, ultimately the baby will come out of her body, but it's still *our* child.