I find it interesting that, according to Mosaic Law (Exodus 22), abortion was only murder if the fetus was "formed". St Basil's assertion that the "formedness" of the embryo was irrelevant seems to mark a break with that line of thinking. My impression of what most people in the West today believe about abortion is that it is something along the lines of the Exodus prohibition: if an embryo is not obviously human in form (generally, if it's in the first trimester), people don't feel like aborting it is killing a person. After it starts to look like a human being around the second trimester, people generally object to an abortion. The general idea seems to be that personhood flows from consciousness, and it's not plausible to think that an embryo in its early stages is conscious. The traditional Christian view is that an unformed embryo is a person since it has the potential for consciousness.
I've come across arguments that the embryo is a person because it is genetically unique, but according to that reasoning, identical twins would participate in the same single person, which obviously can't be right.