You can't compare the UK to switzerland. Guns are probably shown to both increase and decrease different crime rates, and I don't understand what you mean by criminals no longer fear threat of deadly force."
As for the comparing of nations, certainly no two nations are alike, but if the premise is that greater legal availability of firearms leads to higher crime, there are enough examples to provide a reasonably valid sample. Countries with fairly liberal gun laws (I.E. easy for law abiding citizens to own or even carry concealed firearms) include Switzerland, Finland, Canada, Germany, Austria, New Zealand, and also Yemen and Serbia. Violent crime is low in all of these nations.
Yemen and Serbia - why those are hotbeds of violence are they not? While they do have bloody recent histories, and Yemen in particular is deplorable in its treatment of women, violent crime within those nations is very low.
By contrast, India has the 3rd lowest per-capita gun ownership ranking in the world, but the world's highest murder rate. Columbia has the 7th lowest gun ownership rank, and I think we all know how violent and crime-addled that poor nation is.
Clearly more is going on than just the availability of guns. In the case of Columbia and also the United States (which I purposely left off the list above) drug cartels and gangs fighting the police and amongst themselves are an enormous source of violent crime.
But back to the issue of how legal gun ownership affects crime rates. From a criminal's perspective, if you know that there is a chance your intended victim may be armed, would you be more or less likely to attack? The crime-reducing effect of legal gun ownership is extremely well documented in the works of independent criminologists John Lott and Gary Kleck, both of whom have recieved awards from the society of criminologists for their works, which have been peer-reviewed and stand up to rigorous study and questioning. The simple fact is that when law-abiding citizens are permitted to keep and bear arms, crime, particularly violent crime, decreases. It's also important to note that what we are talking about here is not issues of vigilante justice or "wild west" shootouts between criminals and citizens. In the 39 U.S. states which now allow citizens (following varying degrees of registration and training requirements) to carry a concealed firearm, this effect has not resulted. Another important fact, revealed by the works of Lott and Kleck is that in 98% of cases in which a potential crime victim responds with a firearm to an attacker, no shots are fired. The attacker simply flees. (this statistic is from 10 years of data from the FBI's national database of all reported crime).