I personally am a bigger fan of the Bismarck model of universal coverage (Germany, Japan, Switzerland) than I am of "single payer" (Canada) or the Beveridge model (U.K.)
It's curious how often Americans commentating on social policy assume that such 'models' exist, as though social policy is largely shaped by imposing and mutually exclusive frameworks that were freely chosen by policy makers at some point in the past. The reality is different; social policy mostly reflects the social and political pressures within society. The concept of models is an abstraction and a fairly unhelpful one; healthcare systems don't differ in Britain and Germany because they have adopted different models, but because in the mid 1940s the conditions existed for a universalist system in Britain (but not anything based on social insurance or means testing), while in the late 1940s the conditions existed for maintaining and developing exist systems of social insurance in Germany (but not for attempting to build a new socialist welfare/health system).
You could never simply import a 'model' from abroad into the U.S because the social and political conditions are so different. Something like the NHS could never work in America so long as Americans are happier answering intrusive personal questions and accepting that it is right that access to quality care is broadly determined by 'the market' than they are with the concept of waiting their turn or being assessed almost entirely on professional grounds.
