Seeing as I look most favorably on the health care system of France, I voted the "Bismarck Model." Still, it's worth bearing in mind I am influenced by more than one model and tend to mix them a bit.
From what I understand (which may of course be flawed), there is public insurance for everyone but co-pays which reduce the detrimental impact of moral hazard. The state reimburses some of those costs (35%-100%) in some instances in an effort to encourage folks to take cost-effective medications, seek preventative care, and get treatment for chronic conditions that will otherwise worsen in their severity over time (which threaten to become more financially burdensome for both the system and afflicted individuals). The public plan is only basic, so most folks get supplementary insurance privately through their employers. People who cannot afford it receive state assistance. There are public and private hospitals and care providers alike from among which one may choose.
Then again, it would be quite helpful for me if someone from France were to explain some of the pros and cons of their health care system, seeing as I have only read about it through American authors.
You summed up the main traits and I don't really know the details of the French system. One of the recurring problems pointed out about the French system is the tendency of doctors to prescribe excessively. Since they are reimbursed by a public insurance, patients tend to ask for medicines even in cases they are not needed. And since doctors exert their profession privately, they tend to second their "clients"' desires. That's why recent reforms have focused on putting a heavier burden on the purchaser, with the obvious problem that poorer people might actually renounce to useful medical acts. The health insurance agency (like the other branches of France's social insurance agency) also has a pretty huge and ever-increasing deficit since the early 2000s.
There is also an issue with the universal insurance for the poorer, the so-called CMU. It seems that reimbursements through the CMU are slow to come, and many doctors outright refuse to perform medical acts to the people covered by it (even though it is illegal).
In short, it's not a perfect system, but it works relatively well and allows to erase most of health-related inequalities. I still prefer the British model, though.
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