Check out the CONCORD study, which compared cancer survival rates across 18 countries.
The US had the highest overall survival rate (73.8%). Countries with government-run medical care, like UK and Denmark, had the lowest: 51-52.8%.
The difference is especially dramatic for prostate cancer, where the US has a 92% survival rate, Australia and Canada were at 77-85% [1], and Denmark was at 38%.
http://www.ncbi.nlm.nih.gov/pubmed/18639491
(Australia and Canada = roughly, countries where hospitals are run privately but the government pays for more than half of all medical care.)