Before I launch into this I should point out (and this is in addition to the usual caveats) that as far as I know ‘’all’’ systems in Western countries are heavily influenced by the state.  In the US (supposed by many to be the exemplar of free-market capitalism) there is MediCare and MedicAid and the infamous Food and Drugs Agency plus all sorts of other laws and legal precedents.  In France, all employees have deductions from their pay - though, as I understand it, they have some choice in where it goes after that.  In Japan, all citizens are covered by compulsory national health insurance.  The amount of freedom ranges from very little indeed to virtually none.

Even so, as I understand it, the NHS compares badly.

So, the NHS isn’t as good as the systems found in other countries?

I confess I am by no means an expert on this one but the NHS seems to have far more problems than the systems found in the US, France and Japan

Not as good as the US.  But, surely, in the US the poor don’t get treated?

My understanding is that in the US healthcare is more or less universal.  There are government insurance schemes for the old and the poor

Not as good as Japan?

This is based on personal experience and from (as far as I am aware) the lack of anything like the same level of horror stories.

How can you be sure that the Japanese system is (as you claim) freer?

Fair point.  How do you compare (in terms of freedom) a fully nationalised system ie UK with a partially nationalised system with compulsory medical insurance as in Japan?  It is not as if we can measure freedom in milliliberties or something. Actually, in this case, I think we can be pretty sure that the Japanese system is freer in that hospitals and other medical centres have more freedom to do their own thing

Further Reading

Europe has the answer to NHS woes, David Green, makes some comparisons.
Waiting here and there.  Some international comparisons.

Nothing yet but you never know...