The Current US System is the Worst possible system a culmination of decades of government interference in both employment laws which is irrevocably linked health "insurance" with employment and turned "insurance" into a services prepayment pozi scheme.
Government run systems control costs by having a Fixed Budget, which means each year they outlay X dollars, so if for example there are 100,000 Hip Replacements budgeted for the year, and your Number 100,001 well your SOL. This is called rationing... this is one way government control costs. the other is ignoring or limiting patents for drug companies, so drugs cost less overseas then in the US. There are 1000's of things like this that make the government run systems appear "cheaper".
Cost is not the only factor though, Quality of Care is very important and the US still has more Health Tourists than any other nation... there is a Reason for that.