Remember also that South Africa is suffering tribal wars right now. Still, the overall violent crime rate is nearly the same in all three countries, while the rates of other crimes are widely divergent. Regional comparisons for Asia and South America were not possible with the data I could find. Comparisons among European nations, even with mountains of readily available data, are difficult since most of Europe is anti-gun. Within-country information, however, supports the inverse relationship.
Rightist commentators can make several crude comparisons that support the inverse relationship.
Generally, there is more gun control in Europe, and less violent crime, than in America. The real question is whether, holding other things constant, adding guns in the hands of law-abiding people reduces crime. Whether between nations within a limited region, or within any single nation, the data from around the world support the inverse relation. A final point remains to be made about the example of Norway, where there is strict gun registration but otherwise lenient laws and relatively high gun ownership. Crime is low there.