There is a link to lower violent crimes with high gun ownership. Usualy it is replaced with hgiher property crime rates.
That means the number of criminals remains similar, but more focus on targeting property that won't defend itself rather than people.
I however think arguing based on statistics is fruitless. There is favorable statistics to both arguments that pass the logic test to me. The real difference is freedom and liberty. The free people allowed to defend themselves have an extra option, the unfree must face the situation without that option. Sometimes that means the same outcome, and other times it means they die, are victimized, or must watch as a group of punks victimizes thier family or them.
Criminals will usualy be armed anyways, whether with a firearm or other weapons. And if there is multiple armed young male criminals and just a lone victim or a lone family without a firearm the odds are stacked in favor of the criminals getting what they want. Sometimes they just want money, other times they want something much worse.
Do you like options and control or do you trust the criminals?