Its a mixed bag. Notice that Dallas is 20 and Washington DC is 45 ... yet Washington DC has outlawed gun ownbership, but not so in Dallas ... so it is obvious that outlawing guns, in and of itself proves nothing ... another case stufy in Florida, after they instituted conceal and carry laws, the crime rate aganist local citizens dropped 90%. In a town in Wshington State where I lived, you could carry a side arm in a holster like the old west ... we had no gun crime ever ... and only one shooting when a police officer mishandled his won gun and shot himself in the foot. So, I think it all depends on a number of factors besides gun laws.
If the criminals are aware that private citizens are trained, conceal and carry, and will use firearms, and are protected by law, then the criminal will be impeded or chose another area to terrorize. But where the laws are confusing or restrictive it can lead to higher crime rate ...
... yet, in other areas, like the statistics show for London, the homicide rates are lower ... but I think that it has less to do with anti-gun laws and more to do with British civility ... in some cultures, they have low crimes rates with little gun ownership, it seems, not because the anti-gun laws work that well, but because the culture of the indigenous people is that way for some reason ...
... for example, the above statistics do not address robbery and burglery ... for these rates may be as high or higher than other contries where the home-owner is protected by firearms. The criminal knows that can rob and mug and get by with it because the innocent victim is not allow to really defend themselves. So, okay the murder rate is down, but the mugging rates are up ... how much better a life is that?