Hm. Interesting. You know what? Maybe we should switch over, see how men like the discomfort of childbirth.
Of course, women would lose the things that go along with being the childbearing sex. No more "women and children first" on a sinking ship. Women would be sent into combat, and start taking dangerous jobs, too. You know those guys who died in the Batman theater shooting because they were protecting their significant other? That's hardwired in to protect the ability of the species to reproduce. If both sexes can have children, then that would have to go away. The instinct to protect women would be replaced by the instinct for self-preservation.
What you propose would completely change our society, but it would be interesting. Are you sure that most women want to sign up for these changes, though?