The bottom line: I prefer the NHS to the American private system. It's a little more inconvenient in terms of appointment times, but due to the fact that it is free, has no paperwork, and the treatment on the day is super-fast, the NHS wins. That Rolls Royce is moving at a pretty decent clip.
And, of course, there is the small matter of the fact that the NHS covers everyone equally, whereas Americans get care based on their ability to pay, leaving tens of millions with only minimal access to care. (Obamacare is changing that, but it's leagues behind the NHS if you're comparing them by the standard of universal full-service coverage.)
Americans think they have the best healthcare in the world. Take it from me, a fellow American: They don't.