I have to disagree. Armed criminals have an advantage over unarmed police, being armed or not scarecly chnages the balance agaisnt armed police. Police are far more willing to shoot first and ask questions later if there is any hint an assialant or other suspicious person is armed. Police also tend to significantly out number violent criminals, in practice. Getting into a confrontation with armed police, even if you are armed yourself, is quite often a fatal mistake. I'm sure some criminals would feel compelled to arm themselves against police if the police beacame armed, but this would be a rarity.
Armed criminals are more common in the US not because of armed law enforcement, but becasue of the prevalence of weapons. The US is saturated with weapons. Supply is huge. It's really easy to get guns, illegaly anyway. Small firearms are common enough to be nearly disposeable over here. This is also why no gun laws have been effective, they do nothing to change the supply, or remove the firearms already in play (indeed, such as task would be impossible) and the criminals obviously don't care if their firearms are illegal, most have more important things to worry about.
When police do come upon a crime, or have the need to arrest some one after the fact, being armed will geive them a greater chance of success, even when going up agaisnt an armed individual. Unarmed police are at a disadvantage against even unarmed assailants. It's harder to out run a bullet than to out run a police officer. Being confronted by a pair of police with clubs, peperspray, or tasers, is far less intimidating than being confronted by ones with guns, esp if they seem ready to end your life if you flinch the wrong way. Guns inspire more coperation, more quickly than just about anything, criminals know this, the government and police should figure it out too.
The vast majority of criminals also attempt avoid police when commiting crimes and to avoid conflict with police period. Armed citizens are, in all honestly, far more of a deterrent than armed police. If I'm going to rob someone/some place, I won't be doing it when police are looking over my shoulder, or close by. The fact that any given residence in my country has a good chance of having a firearm of some sort makes people think twice before breaking in. Many a burglar has come through a window only to endup face to face with the owner and his or her firearm, or dead from a wound delivered by such.
Realisitically I think a society either needs to have no guns (at all, with very few exceptions), so no one can get them, or the majority needs to have access to them to beable to defend themseves from others (wether that be criminals, abusive police, or members a potentially oppressive government/military) that do.