I mean, this is a fair philosophical matter, but your definition of personhood shouldn't bleed over to restrict woman's rights. Women who don't want abortion are free to not do it. Women who want abortion should be able to get it.
If the definition of personhood used to prevent us from killing coma patients also encompassed a fetus' right to life, then it would require special pleading to have legalized abortions. If this was true, the fetus' right to life should supercede the woman's right to choice. So if philosophically we cannot find a justification for allowing abortions while respecting coma patients right to life, our legal code should follow. The justification for women's rights are at their base, philosophical. So if abortion fails philosophically, a woman's right to choose does not encompass abortion.
However, I've been thinking more and have changed my mind on the definition. Thinking about a case in which a woman's life was endangered and could possibly die if an early fetus wasn't aborted, I realized that my earlier definition of personhood would leave her the choices of either dying or being a murderer. This didn't sit well with my moral intuitions, as I still see the fetus as at least less of a person than the mother and extending full rights to the fetus led to absurdities like the previous case.
I've also been watching lectures by Shelly Kagan on the philosophy of death. His theory of identity is probably the best I've heard of and can potentially reconcile the two cases of the coma patient and the fetus. His theory of identity (personhood) is contingent on whether a persons personality is functioning. Of course, every time you go to sleep or get knocked unconscious, your personality stops functioning, but he gets around this by making a distinction between a personality being turned off, versus not being there at all. In a patient in a vegetative state or a fetus, the underlying structures of personality are simply not there at all, versus in a coma patient, even when higher brain activity is not working, the personality is still there but inaccessible (turned off).
The implication of this is that abortion is not murder if we are talking about the early stages of pregnancy. If the fetus is not to be considered a person under this definition, a woman's right to choice wins. However, I think this only applies to early stage pregnancy (first trimester), as I'm not convinced by the science that there is no sentience (personality) at all in later stage pregnancies and I think it's best to err on the safe side when it comes to life. I also think that failure to use responsible birth control leading to an aborted pregnancy is morally repugnant, but doesn't supercede a woman's right to choice.
Topic: Secular Pro-Life Debate