The US pays more money because it has more health care being provided, in many cases.
It just so happens that more health care doesn't necessarily translate to measurably better outcomes (e.g. cancer screening helps reduce mortality for some cancers but not others).
It also just so happens that it's very rare to study whether a particular care regimen actually improves overall outcomes as opposed to just the thing it's ostensibly aimed at treating. Continuing our cancer example, cancer screening helps reduce mortality from _cancer_ for almost all if not all cancers, but for some the increased mortality from operations and other cancer therapies cancels out the improvement.
That's not to mention the fact that people in the US prefer to get care even if they know it'll likely make them worse than not getting care. I'll dig up the reference for this; I don't have it offhand.