I work with people who do iPS (induced pluripotent stem cell) work. The technology is quite promising: take a skin punch biopsy, add Yamanaka factors, and obtain iPS cells. They have not supplanted embryonic stem cells for most purposes but someday they may (there are various scientific advantages and disadvantages to both).

I think the most honest answer is that even those of us in this field don't yet know if storage of cord blood will prove to offer something that iPS can't. Perhaps there is someone even closer to the intersection of those topics than I on HN who can weigh in.