How does the level of coverage in countries with single-payer health insurance compare . . . ?

with the typical insurance policy in the US?
--------------------
I have lived for a number of years in two other countries that have single payer systems and since last year with Medicare here, which amounts to the same thing. In all cases it's a good idea if one can afford it to take out supplemental insurance. In all cases the system worked just fine for me and a great deal better than the insurance I had from a private insurer in the US before I became eligible for Medicare.
Source