If you can afford private care, and are lucky enough to have good insurance through your job, you'll get better care in the US. Not in terms of quality, but in terms of wait times, and how nicely people treat you. I think the actual medical interventions are just as good either way.
I don't know if it would be possible to have it both ways. Give universal health care that's decent to all, yet give even better care to those willing to shell out extra.
I know in Canada its always a big debate. Some people think a hybrid public/private system could do it. Others worry it will just marginalize the affordable health care and lower its quality and increase even more its wait times.