To say which country has best banking system depends on whether you are measuring freedom of operating, legislative control, supervision or accounting methods.
Almost all banks in the European Union use the same methods so there is no real choice there. Banks in the USA are generally more closely monitored than in the rest of the world. China is a special case, since all of the banks there are largely state-owned and are very tightly controlled.
Listing the countries with the safest banks depends on the cut-off level in the rankings, if all banks ranked at a minimum of Axx are counted, then Canada with 6 ranks ahead of the USA in North America. In South America, Chile with 5 banks outshines Mexico and Peru with one each.
In Western Europe, Germany has the most safe banks with 4. Switzerland, Netherlands, Norway, Sweden and France each have one. In Central Europe, Poland has 3 banks and the Czech Republic one. Some of the largest banks in Asia Pacific are, Singapore and South Korea each have three banks, China has two, with Hong Kong and Taiwan having one each. In the Middle East, UAE has four banks, Kuwait has three and Israel and Qatar each have one. Australia has 9 banks and New Zealand has one. There are no banks in Africa rated above BB+.
It is difficult to say which is the safest bank in the world, since all banks rated at AAA are generally regarded as being equally safe. In one respect, we can choose which banks are the most secure based on the size of the bank, in which case, KfW in Germany which has assets of more than $550 billion.