This really is the main crux of the issue, revolving around morality, and the definition of what constitutes a human being. The Pro-Choice side is more secular, defining human beings by biological criteria, the Pro-Life side defines human beings by a magical essence. Pro-Choicers are almost universally consequentialists, utilitarians, whereas Pro-Lifers tend to be deontologists, believing in an absolute morality derived from scripture.
While we're talking about compassion, it's worth noting that Pro-Lifers are significantly more enthusiastic about war, capital punishment, and torture, than Pro-Choicers. Since you mentioned it.