Was wondering, what determines whether the CD or the vinyl version is the primary issue of a certain release if they were both released on the same day? Headless Cross for example has the CD edition as the primary, what made MA decide that would be primary instead of the vinyl one?

Assuming the vinyl isn't a limited/special edition or something, there isn't really a standard for that. It doesn't matter, all other things being equal.

So the first listed edition is just more coincidence than anything else regarding multiple formats on the initial release date?

Pretty much.

In the case of Headless Cross, when that album came out record companies were putting vinyl on the back burner and pushing CD format. In that case, I'm sure that the CD was the primary release format from what I remember.