In Spain we also have public and private medicine, but in my experience neither is better across the board.

Private medicine is better for ordinary care (family medicine and ambulatory treatment) but private clinics and hospitals are not as good as public ones, the reason being that private clinics cuts corners for profit and public hospitals are more often associated with Universities.

Opponents of socialized medicine in the US (well, in the US advocates call it "single-payer system" because they need to avoid the word "social", but I digress) often point out that Canada has fewer MRI machines per capita than the US as if that single statistic captured all you need to know about health care.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman