Which is more likely. Show your stats. Doesn't mean it can't happen, just show your data and let me determine which are better odds. Not your decision to make.
I'm not saying it is my decision on what you do. You should avoid saying that I am making a worse decision for my family because I rely on the police to respond to a burglary. If you own a gun you assume many other risks which you happen to be ok with.
In 2011 in Charlotte there were 6,300 residential break ins and 55 murders in a population of of 757.000 and 341,000 households.
Less than a 2% of a break in and a .0000726 % chance of being murdered