Generally speaking, lawful use of deadly force is lawful use of deadly force. The type of weapon should not be a factor, though in some jurisdictions it has been presented as one.
But C0untZer0, you are conflating two separate issues.
Florida has restrictions on the types and calibers of firearms that security guards and private investigators can carry, while working. CCW permits do not supercede those rules.
For instance, with my Florida permit, I can conceal a virtually unlimited array of weapons, so long as I can legally own them. (Some states specify handguns; Florida does not.)
But, if I wanted to get licensed as a PI in Florida, I'd be limited to revolvers in .38 or .357, but carrying .38 ammo; or autos in 9mm (and I believe .380), while I was working.
After work, I could carry my .45's to my heart's content, but not while working under the auspices of the PI license.
Same concept for security guards.
Has no bearing at all on what you, as a private individual, could use.