Gathering statistics and comparing them across systems could be done, but a final ranking of the systems to determine the "Best" system in the world would be (at best) arbitrary or (at worst) entirely political ...
The United States is probably the hardest country to really judge the quality of healthcare system because the top 25% of patients receive the best treatment in the world, the middle 50% receive healthcare that is on par with most other western healthcare systems, and the bottom 25% receive no/poor healthcare services. If you were to jude the system based on the top 75% of people there is no system in the world which is competitive with the United States ... at the same time, if you look at the bottom 25% only the United States is a nightmare.
Now, you can look at the bottom 25% and say that the free market system has failed them and the government needs to step up and provide worse service (on average) for the other 75% of people ... Or you could look at trying to solve the core problems that are driving up the cost of service beyond the ability for a large portion of the population to have adequate service. I would personally suggest that you solve the cost issue because after something becomes run by the government and is full of pubic sector unions you will never be able to make any efforts to reduce the cost.