Comparing costs is a tricky business. For one, they have limits on the available locations and types of procedures covered by a single payer system. Generally lower quality care and rationing of services is what you get. Its inevitable to control costs in that system.
I think the costs could be much lower if patients had a choice of which procedures and where the get the procedures done.
Here is an example... my insurance company covers the colonoscopy procedure at 100%. My doctor, who is a standup guy, gave me two choices for the procedure. One at a local hospital which charges over $3500. Or another medical center a little farther away for only $1500. Same procedure and anesthetics but a $2000 difference because the other place can get away with it. What we need is reform and transparency of the medical procedures and the ability of patients to shop for the best option for themselves.
I do think that if congress would pass a law allowing insurers to sell their product across state lines, force the service providers to publish the itemized costs of all procedures, and add all people not currently covered by private insurance to an "Open Pool" that a quasi private/federal insurance company (think Fannie Mae/Freddy Mac) to sell minimal catastrophic insurance to. That would enable market forces to control costs and cover those who want insurance but cannot afford the private market plans.