Assuming there is no workaround the issue, e.g. a sit-down with both authors did not solve the issue, this is how I have seen this solved:
The paper is split into two papers, one paper with authors A, B, the second paper B, A. The fight then moves on to which paper will take the lion's share of the contributions from C, D, E, and F, assuming that A and B will each try to have their respective papers be the bigger one. So C, D, E and F have a conversation without A and B present and split the baby (https://en.wikipedia.org/wiki/Judgement_of_Solomon). Nobody is happy, but everyone moves on.
Both papers are submitted simultaneously with a note to the editor. This requires a compliant editor, which might mean a lower-ranked journal. But that's the price A and B have to pay. I've seen this solution work a couple of times.
But let's assume that they both dig in, neither wants the paper split, and both want you to adjudicate. As @sErISaNo notes, A is in the right.