On an average american citizens spend $8700/year on healthcare, while all other OECD nations spend less than $6000/year/citizen. (2015, sources : United Nations, OECD.stat, oxford university)
Also at the same time, all other OECD nations have a longer life expectancy (79 for the US, 81 to 84 for OECD countries).
The main difference is that the State isn't trying to make profits out of healthcare, the money is entirely dedicated to quality and access to the service, and if there's a surplus, it goes into improving/developping other public services (education, police, infrastructures, housing, ...) or into tax reduction.
In a privatized system it's just another business, where, as a business man, you try to make profits so the surplus of money is going to shareholders instead of being re-invested or price reductions. You're no longer a patient, but a customer.