A generality: Areas where the people are less likely to commit crimes tend to have less restrictive laws. Less perceived need for more controls. Areas with higher crime rates tend toward calls for more restrictive laws.
While the CHL laws may not have direct impact on crime rates, they do change criminal patterns, as was discovered in Florida. For instance, even before the carry law was passed in Florida, there was the Orlando experience:
There had been instances of public assaults on women. The police publicly offered a handgun training program for women, with a fair number of women attending. The publicity surrounding this apparently scared off the would-be bad guys, as the rate of assaults fell toward zero. This was in the 1960s, I believe, although my memory is a bit rusty.
After passage of the Florida carry law, muggings declined. Car-jackings shifted to rental cars, particularly those from airports. Interviews with arrestees indicated a knowledge that incoming tourists wouldn't bring guns on a plane and were thus safe targets--but local residents might not be. The same results obtained when the particular issue was robbery at highway rest stops and out-of-state cars.
Further, after a CCW cab-driver shot a would-be robber, robbery attempts on taxicabs fell to a much lower rate.
My own conclusion from this sort of data is that if all states had CHL/CCW laws, and some percentage of the people availed themselves of the licensing, the increasing uncertainty for would-be criminals would shift them toward patterns of less risk--and, possibly, less violence. Burglary instead of robbery, as a for-instance.