Well, that depends. The vast majority of people do not own guns, hence the odds of someone being shot are much lower. (I'd be curious about those statistics as to how many of the crimes were committed with a legally purchased firearm, even one later stolen.) This has not always been the case. We have an image of the lawless West in our heads that isn't very realistic, because it was not lawless. Petty crime was practically nonexistant. Serious crime (excepting saloon shootings, guns+drunks=bad) was extremely rare. The reason for this was that very nearly everyone had a gun and you were very likely to end up getting shot during the comission of a crime, medical care was nearly nonexistant so you'd probably lose a limb or die if you got shot, and hence there was no profit in criminal activities and the recividivism rate was just about zero.
Albeit, there are a large number of places in the world with similarly easy access to firearms, similar lack of medicine, and they are incredibly violent. The likes of Somalia spring to mind, which I guess could be viewed as the ultimate example of what happens with no government as much as what happens with piss-easy access to weaponry.
This probably would not work with the society of the modern US or UK; the simple truth is that the average person does not take firearms seriously enough and is apt to use them needlessly. But there are other countries out there where pretty much everyone owns a gun and they have low crime and low gun violence. Sweden makes a good example. They have compulsory military enrollment, and since you are subject to callup at any time even after your term is up, they let you keep basic kit, such as a fully automatic rifle and some ammunition. There are no Swiss home-invasion robbers when every adult male has an assault rifle in the house. And they take their weapons seriously.
It comes down to training, I think. Anyone who has taken any kind of military or civilian firearms training has had it etched into their skulls that "Hey, this thing is dangerous you idiot!" in a way that somehow countless scenes of people killed by firearms on the TV doesn't. Trained shooters who use their weapons on others (outside of the military) are a very small minority. Everyone remembers the D.C. sniper, but for him there are thousands of others whose training was nonexistant; if nothing else demonstrates that their average accuracy ought to.
Except an automatic weapon itself has its own differences to 'casual' handgun ownership ala the US; for one thing it's not as easily concealed, carried, or used as a loaded pistol. I'm also pretty sure there are - in the specific Swiss example - restrictions and social factors upon gun ownership; such as the need to register all bullet purchases, state the need to own a gun for a specific self-defense purpose to get a weapons permit, required specific permits for carrying outside/in public, and strong military discipline vis-a-vis handling weapons as well as compulsary tests. I'd suggest the Swiss example; a well regulated and trained militia, is rather closer to what the US Constitution envisaged than a 'lets buy M-16s to shoot burglars' type free-for all. And it's also worth noting that Switzerland is one of the worlds richest countries, without the same sort of social problems arising from, say, deprivation as in other countries.
Although Swedish crime rates aren't all that different to the rest of western europe, may I note. (I've not had too much time to go searching, natch, beyond that). But my suspicion is that you'd find you could remove guns from these places, and the crime rate would not increase atall (actually, one strange article I found stated that Swedish medical students were queuing up to study in Pennsylvania - because of the sheer number of handgun shooting victims there).
One offhand aside, though, is that (US) studies have indicated that accidental gun deaths were higher in households with some form of firearms training (police, gun club, or military).
In any case, I still can't see how giving people easy access to a device built for the express purpose of killing and maiming people makes society safer.
