In Mexico, crime is rife. And the firearm law is one of the most severe.
Ukraine has lower crime level, somewhat similar gun licensing.
In the US you are free to buy a weapon and many states would issue a concealed carry permit. That leads to much lower crime rates than in aforementioned countries.
In Switzerland, you may own a full-auto rifle, shoot in all cantons freely. The crime level does nothing to correlate with firearm law.
In the opposite, use of firearms gives assault more protection.