Does ribbon pointing make a wall of masonry stronger than other kinds of pointing?

I don’t know if there are any people who know about masonry here, but it’s worth a shot.

I’m not sure the proper terminology: ribbon joint or ribbon point or what, but it’s a raised line of mortar between stones. The alternative is a regular surface level mortar. My house has ribbon joints, and I want to get it repointed because the mortar is falling out and the previous owners have done a horrible (read by themselves) job of repointing.

One estimate by a high end mason describes in detail, how he will drill out to this depth and then wash and clean all the stone and chip off the mortar a previous owner splattered on. The other estimate just says he’ll repoint it.

The high end guy says that ribbon joints are stronger than the other kind. The other guy says they aren’t—they’re just for looks. The other guy also does not describe in any detail how he will do the work.

Who is telling the truth? Which is better?