First of all, you have to realize that those allegedly private health care systems in the US and Switzerland are still far away from what a real private system would look like. The governments of both countries heavily regulate insurance companies and their products to make sure that every citizen gets almost full coverage (All-You-Can-Eat principle) and they reduce competition between insurers.
Secondly, it is very important to understand that the different types of health insurances around the world all exhibit the same major problem: they aim for maximum coverage and try to eliminate fees that are correlated with the amount of services consumed. So they all give incentives for overconsumption. To be precise, an insurance that covers every possible expense is not an insurance anymore, so it is kind of misleading to call some of those systems „insurance“. Anyway, for the sake of simplicity and comprehensibility, I shall stick to this common term usage.
Now, compare countries that are similar with regard to health status of the citizens and culture, i.e. eating and general living habits, for instance Great Britain, France, Germany, and Italy. The difference between the most expensive (France, 11% of GDP) and the cheapest (Britain, 8.4%) is approximately 25%. The French system has big problems with overconsumption, especially of prescription drugs, due to the fact that patients still have free choice of doctors and co-payments aren’t high enough to deter overconsumption. The government and the insurance companies didn’t introduce rationing yet. Instead, they rely on private insurances to take off some pressure from the system.
The NHS of Britain also encourages overconsumption due to the fact that patients do not have to pay a penny at the counter, since everything is financed by taxes. So the government simply rations health care in several ways: it takes expensive pharmaceutical drugs off the market; hospitals are overcrowded and understaffed, so they simply don’t offer many treatments; and practitioners keep patients away from hospitals or expensive treatment in general.
So it is very surprising to see that, despite heavy rationing, costs are still only a relative 25% down compared to France. It is reasonable to assume that costs would be even higher than in France without rationing, which is in line with what economics would predict, as the British system has even less hurdles for overconsumption than the French. By the way, the same comparison, with the same results, can be made for Germany and Italy, with Germany taking the role of France and Italy that of Britain (Italy copied the British NHS in 1978).
Let’s have a look at the US and Canada, two arch enemies with regard to health care systems. The US consumes 16% of GDP for health care, Canada only 10.1%. So Canada saves proximately 38% over the US. Just like the British system, the Canadian system knows no barriers for overconsumption, were it not for the heavy rationing of the supply of health care. The US system has also comparatively few incentives to control consumption, since co-payments are often very low and employers pay the biggest chunk of premiums. It seems that Canada is more successful in cutting costs than Britain, but there are several factors, that are responsible for this misleading image.
Firstly, Canadians tend to be healthier than Americans, which is probably mainly a result of cultural differences and eating habits. Secondly, the US has a 25% higher GDP than Canada. Economic theory and empirics tell us, that health care will take an ever bigger chunk of consumption expenditures with rising income, as affluent societies can easily afford basic consumer goods and have increasingly higher (relative) preferences for health care. So, if we crudely adjust for the aforementioned two factors, the difference between USA and Canada becomes much smaller. The remaining difference is contributable to the rationing, just like in Britain, where it perhaps saved over 25%. This should explain the „Canadian cost miracle“.
Finally, let’s have a look at Switzerland and The Netherlands. These two countries rely solely on private insurances, which are heavily regulated to offer broad coverage for many important treatments. If someone wants even more extensive coverage, he can choose to buy additional private insurances. The most important features of both countries are, that the insurances have high deductibles (up to thousands of Euros) and that there are relatively large co-payments to pay (several hundreds of Euros per quarter). This keeps consumption at least a little bit in check. And the results can be seen in the table above. Although Switzerland and The Netherlands have the second and third highest GDP in this comparison (Norway is on top), the share of health care of GDP is only 10.8% and 9.8%, respectively. Further, Switzerland probably has the highest incomes for physicians in Europe, so you may want to adjust the data for that fact, too. Most European countries are massively suppressing physician incomes in an effort to reduce costs.