Well, I'll give my opinion, but I could be wrong.
No brain?!? Well, in that case, I'd be hard-pressed to call the baby a "living human." Sure, there are living human cells there, but is there a living human altogether? I'd say no, because the level of sentience involved is near zero. In any case where the baby inside is non-living/entirely non-sentient, the decision would default to the woman, since she has a non-sentient husk of a baby inside of her (but not an actual sentient baby).
Who
should decide? Some omniscient entity should decide.

Since no
verifiably omniscient entities are speaking up about it, we're stuck with forming some kind of reasonable consensus...one which I feel should generally err on the side of assuming the baby is alive in cases where there's any strong indication of such.
A zygote is a living human cell, but I'd be hard-pressed to call it sentient by any reasonable standard...while the more religious/dogmatic pro-life types disagree, I really have to say no on this one. Here again, like with the brainless baby, the decision would default to the woman...but
only because of the lack of sentience. (One sentience enters the picture - which I'd place around the time the higher brain functions form and the heart starts beating - that's when my answer changes dramatically.)
As above, we're stuck with second-best when it comes to who should decide.
Location changes this because society collectively picked "baby's first breath" as the moment that life/sentience begins...and it sounds so inconsistent precisely because drawing the line in the sand there is hopelessly arbitrary. From the baby's point of view, first heartbeat and first brain waves are
much more significant than first breath.
The line wasn't drawn there because it actually makes sense with respect to the baby's level of sentience; the line was drawn there simply because it's convenient to pro-choicers and abortionists to claim everything dependant upon a woman is fair game for the blender.
Who decides? There's an objective universal truth here about when life/sentience begins, but it's unobservable to us, so we're stuck with our subjective opinions, unfortunately. Even more unfortunately, criminal law
must take a stance on it, either actively or passively, and a lot of people are going to disagree with that stance, one way or another (by taking "no stance," it would be taking a pro-choice stance by default). For lack of a better way, taking a vote on it and going from there is sadly the "fairest" approach we have for reaching consensus...and considering how much I disagree with today's prevailing opinion, it's apparent just how much faith I put into our most reliable available approach.

In the practical sense: Because of our limited knowledge, the wide margin of error, and especially the horrendous implications of assuming life begins later than it actually does, I think it would be best for all involved if we all decided the issue more locally. That way, local communities would at least better uphold individual rights in a way more consistent with the views of their inhabitants.