Stem cells from cord blood are perfectly suitable for a transplant if they are a match for you. Because cord blood units have only a small quantity of cells, a single cord blood unit is typically sufficient only for a child or small adult. An average adult would need two (or more) matched cord blood units.
The
National Marrow Donor Program website summarizes what researchers have found about the differences between cord blood and stem cell or bone marrow transplants. Research seems to show that cord blood doesn't have to be as good a match for a successful transplant, and graft-vs.-host disease (which often results from transplants) tends to be less severe with cord blood. On the other hand, stem cells from cord blood tend to take longer to engraft so there's a longer period where the patient is at high risk of infections.
Those tradeoffs matter only when you have a choice. When you don't, the goal is to find a match for any kind of transplant. Good luck finding a match in the cord blood banks.