Papers are for more than status. They are for more than proving a dog is purebred, though that is one of their advantages.
They are a blueprint for the genetic history of the dog. Knowing the dog's pedigree allows one to research the health and temperament of it's ancestors and other close relatives. This is imperative for making good breeding decisions. Many problems, both health and otherwise, are polygenic and recessive, meaning that they can be hidden in an individual dog in the sense that that dog does not express those problems, but the genetics for those problems are still there and may well come out in offspring. Researching the pedigree will provide insight into what problems exist in the line, and thus could possibly exist in the individual dog.
Without papers, you can't know the pedigree. Without knowing the pedigree, you can't learn the genetics of the bloodline and relatives, which provides important insight into what the dog might produce.
Since there are plenty of dogs being bred who have BOTH health certs (and performance titles proving temperament) as well as papers and documented pedigree, my answer to your question is neither. There is no reason for anyone to settle for a pup from unpapered, and thus of unknown heritage and bloodline parents, or for a pup from untested parents.