I lived in France for a few years with my work. They have a byzantine system - kind of really confusing in a way that the French have turned into an Olympic sport ... but the dis quietening thing was that whenever you went to a doctor, the first thing they would prescribe was a suppository. Never worked out what it was that made them think that part of any treatment - for a sore throat, a cut finger or what ever, was to shove something up your ass. Odd. Still, they never turned me away for treatment. And I avoided the superiority.
Then I was posted to the wonderful land of Oz. They have a national health system - a bit like the NHS in the UK - that the population like and want but which the conservative governments want to dismantle and go to an American model. WTF. The existing system kind of works, its just under funded. But I have to say that I had to attend hospital a couple of times (spider bites, attack by a dingo, hit by a drop bear, that sort of thing) and well, I was seen and did not pay for anything. They did not want to go near my ass.
I saw a GP a couple of times. You can pay them (It's about $80 per consult) - but the govt refunds about $40. Or they just send the bill to the govt; you pay nothing and the govt gives the GP about $40. It seems to work. So, in answer to your question:
The French system if you want treatment and confusion, and things stuffed up your ass;
The Oz system if you want treatment by a bunch of people who are pretty laid back, underfunded and kind of wondering what they did to deserve living in Oz.
There are wait lists for elective surgery as a public patient, and if you have insurance you can get it quicker. But emergency surgey is done right away and they dont give a fuck how much money you have. Most cancer treatment is more or less free. It's a really strange place that breeds a kind of apathy.