This difference is certainly intriguing, but, like many other general ‘why?’ questions, can be approached on different levels.
Because they evolved differently.
is one answer, and not a trivial one because of the shared cofactors of archaea and eukaryotes. But I imagine that the poster would respond by asking why they evolved differently — whether there is some functional or structural difference that can explain this. There isn’t, and the question is avoided in the papers I have looked at, so the answer would seem to be
Nobody knows. If there is a reason it is not evident from the function the reactions perform (which is the same) or the structure of the enzymes (which is similar at the active site).
Let us look at the thermodynamics of the reactions. In both cases a phosphodiester bond is being formed, a reaction with a high +ve ΔG. In ATP-dependent DNA ligases an overall –ve ΔG is achieved by the hydrolysis of ATP to AMP and pyrophosphate; whereas in the NAD-dependent DNA ligases it is supplied by the more unusual, but equally energetic, hydrolysis of NAD+ to NMN+:
The overall structures of the two types of DNA ligase are different:
But the catalytic site for the ligation reaction is remarkably similar in both cases:
(Both diagrams from Structure 1999, 7:35–42)
So explanations in terms of mechanism of reaction would seem to be ruled out.
There are several analogous problems in biochemistry, e.g. why GTP is generated in the tricarboxylic acid cycle in most (but not all) organisms, and why NADP is the cofactor for a particular oxido-reduction reaction in bacteria, whereas NAD is used in eukaryotes. In general one feels (or at least I do) that the explanation must be something to do with compartmentation of cofactors or coupling reactions to their availability. Perhaps a particular choice was advantageous to bacteria early in evolution, but this was no longer the case in eukaryotes, and in fact the reverse became true. But without any evidence to support such arguments they are merely hand waving, which is why professional scientists generally tend to avoid them in their research publications.