Are there any measures of how America does compared to Europe if you only count Americans that have good health insurance? It seems to me that many people who are opposed to socialized medicine don't necessarily disagree that it would give the poor better care; rather they fear that it will result in them receiving worse care.
Anecdotally, I'd say they do crap.
Friends outside LA are upper-middle class. Extremely good health insurance for the last 20+ years. Had a baby, emergency C-section. Less than 12 hours later they were told they must move hospital or else pay the $60,000 per day out of pocket because their insurance wouldn't cover it anymore. They had to drive themselves, in their own car, less than 12 hours after an emergency C-Section, with the infant.
Of of this after paying through the nose for 20+ years for excellent health insurance.
As an Australia/Canadian this is barbaric, and utterly unacceptable.