answer:I don’t know for certain, but it’s not the pointing that lends strength to the joint, it’s the mortar inside between the stones. The big thing is that you need to keep water from getting into the joints, as when that freezes it’ll crack more mortar out. I’d ignore the question of ribbon vs. flush, but cleaning out all of the old mortar is rather important. I’d ask the second (cheaper) guy for a quote for cleaning out the old mortar and replacing it, not just repointing. He may have taken “I just want them repointed” at face value.