Relying on Wikipedia (I believe it is reliable for this purpose, since it in turn uses the Nobel web page), I have calculated the number of scientific Nobel prizes per capita in the post war period. Because the period is 1945-2009 I have used the average population 1950-2009 from the OECD Factbook. Note that Wikipedia double counts people with affiliation to more than one country.
To make it about what everyone agrees are pure sciences, the Nobel Memorial Prize in Economic Sciences is not included. The figures are thus based on only Physics, Chemistry and Medicine.
Not surprisingly The U.S crushes the E.U.15, getting 9.8 per ten million people, compared to 4.7 for the E.U.15. The U.S alone got close to half of all scientific Nobel prizes in the post-war period, more if Economics is included. (I once did the same exercise for U.S alone, including Economics, restricting the country affiliation to what the Nobel home page wrote, and measured those with 2 affiliations as half. The U.S got 60% of all prizes).
It may be just a coincidence, but a good news for Europeans is that the E.U.15 reduced the massive gap with the U.S slightly in the 2000s compared to the 1990s. Not adjusting for population the U.S got 117% more prizes in the 1990s, and "just" 84% more in the 2000s.
What I am really impressed by is Switzerland, who has by far most prizes per capita in the world in the post war period. There is a famous quote from the movie The Third Man that "In Switzerland they had brotherly love - they had 500 years of democracy and peace, and what did that produce? The cuckoo clock."
This is wrong, and an example of the representativeness bias. (Already by the time the movie was made, tiny Switzerland had won 8 scientific Nobel prizes).
Sweden does very well also. Someone could blame this on home bias. The Literature prize for example has an absurd number of Swedish and Nordic winners. Sweden has 6 Literature Nobel winners and the Nordic countries in total have 14! In comparison China has 1 literature prize, the United States 12. For Economics Ohlin deserved it, Myrdal probably did not. I don't have the knowledge to judge the 3 core sciences, but hopefully they are more objective. I personally think even without home bias Sweden would do very well, they are a creative people with a strong tradition in engineering and science, especially before the welfare state started to erode some of their norms and education standards.
The Swiss case aside stereotypes are confirmed. Germany is a science powerhouse, Italy is not, to put it kindly, and France is in between.
Japan and South Korea do poorly, in line with the stereotypes that Asians are smart but not creative. However a more likely explanation is the very long lag between scientific work achievement and prize, in much of the studied period Japan and South Korea were quite underdeveloped.