I don't care much about what system is used, but I'll tell the situation in Holland.
We have had a system of public healthcare for tens of years now. In the last 10 years or so they're slowly privatizing it again. Right now it's sort of an combination of governmental and private.
First of all: everybody has to have a health insurance. At the moment you have to pick a insurance company yourself. Prices, quality, services etc. vary a little, but not much. You have many options, for example a dental insurance.
I pay around €100 a month. I think it's like €90 basis + €10 optional insurances.
Here comes the interesting part: the government finances you, based on how much money you earn. I get almost €60 a month, which is probably around the max, because I'm a poor student.
So effectively I pay €40 a month.
I can go to any hospital, dentist, etc. I want, and give them my insurance information.
I'll have to pay the first €150 of my yearly costs myself, but after that 80%-100% gets paid by my insurance.
I like it.
It works.