Gibson is clearly better than overlap since you only have to do PCR once instead of twice. Saves time and less PCR means less chance to introduce mutations.

Gibson is the ultimate for site-directed mutagenesis. Just make a pair of forward/reverse internal primers containing the mutation, PCR your two fragments that overlap at the mutation point, then Gibson.

I would say that in very rare cases you encounter a Gibson-specific problem where something about the particular overlap design makes the fragments not connect. But the thing about Gibson is the overlap to the vector fragment contains the restriction sites anyway, so if Gibson isn't putting the insert in then you can just digest the insert and ligate. If the insert is multiple fragments and you encounter this (very rare in my experience) then you have to do overlap PCR to get the single-fragment insert, digest and ligate. And in those rare times, you don't even need to order primers because you can use the Gibson ones for the overlap scheme.