… measured how? On what data do you base your claim?

The UK death rates for cancer, stroke and other major illnesses are all higher in the UK than the US. The US also has superior survival rates for cancer, stroke and heart disease as compared /w the UK. Finally, after normalizing the data for violent crime and traffic accidents, the US has a longer life expectancy than the UK.

So, exactly, why do you claim that their health care system does a better job? …

The measure I like to use is called "being alive." That's the most important health care outcome I can think of.

If we use "being alive" as measure, we find out you are more likely to die of a treatable condition or medical error in the United States than in the UK. Not every treatable condition of course. But overall you are more likely to die of a treatable condition in the US than in the UK.

http://content.healthaffairs.org/content/27/1/58.full

As an aside, a lot of people talk about superior cancer treatment in the United States. However, what they are usually talking about is the five year survival rate. It's true that five year cancer survival rates are generally better in the United States than elsewhere. But again, I think "being alive" beats "surviving for five years and then dying." So a much better metric is the mortality rate. The only way to reduce the mortality rate is to either cure or prevent the disease, right? That's what we want. If we look at cancer mortality rates, the US is still pretty good overall but virtually the same as most G8 countries. And for some common cancers like lung cancer, the US is dead last.