I have a similar problem in PA while hiking. Our Black Bears are a tad bigger than Florida. Coywolves and Feral Pigs are a possibility, and there are always bad 2 legged predators, especially with Heroin and Meth being an issue in some of the rural areas.
For both situations you are going to want a handgun that packs a punch and has a round that can penetrate deep especially with dealing with the hide, skull and shoulder blades of a black bear or a large pig. However you want a handgun that is easy to carry, not too big and does not weight too much, especially with running.
While I am no official gun expert, what I have found looking at gel test from people like http://www.brassfetcher.com
is .357 out of a 2" snubbie is not real effective. It basically performs similar 9mm out of a compact pistol. That said "in theory" a hot 9mm FMJ (NATO or Buffalo Bore) or a short barrel .357 will do its part in punching a hole into a medium sized black bear skull at close range if your aim is good. You will get even better performance from a .357 with a 4" barrel, but then you are talking about a serious increase in size and weight. I don't see a feasible way to run or jog with a large steel .357 revolver.
The funny thing is that basic .40 fmj range ammo gives you slightly better performance then exotic +p 9mm fmj ammo with a slightly thicker diameter. 10mm will perform even better, but the pistol options are few, and 10mm has a kick, and ammo is expensive and hard to find.
.45 while it does hit hard and makes a big hole, does not penetrate well through bone and hide especially coming out of a short barrel pistol like the XDs. The velocity is just too slow and penetration is less than 9mm. Not to say it cannot be done with a .45 but the penetration test, and chronograph readings are very unimpressive. Also like mentioned earlier I flirted with the .44 special and .45colt but came to the same conclusion, that they will perform similar to a .45 acp, sometimes even less. Also since .44special and .45Colt, is harder to find, limited and more expensive that .45acp, you are just better of going with the .45acp. However if you go exotic buffalo bore ammo made specially for high penetration you can have a very efficient bear & boar stopper with a 45acp pistol or a .44 special / .45colt revolver
.44 mag would be effective, but again there is not too many guns in .44mag that would be easy to run with, and the ones that are would not be fun to shoot.
That said I think any of these rounds will dissuade a bear or boar attack. We had a few thread running about guns and animals on ZS. There are plenty of stories of Police officers and Civilians stopping all types of bears, bulls, cougars, lions, tigers and even elephants with a basic 9mm/.357/.40/.45 handgun. Most of the time its not pretty, but the animal attack is stopped. Emptying a 9mm pocket gun into an attacking animal and having it lay motionless with a fractured skull and shoulder blade as it bleeds to death is still better than having that same animal tear you apart because you left that .44 mag at home because it you got sick of carrying it.
For me a S&W Shield in .40 is the perfect hiking gun. Its relatively lightweight, compact, and .40 FMJ flatnose seem to be a cheap yet effective round to not only practice with but in a pinch hopefully stop a black bear attack. However I think any handgun 9mm or better, with the right ammo can do the job, but some can do the job better than others. So the only question will be what are you more comfortable with carrying (again we are taking running) and shooting regularly and accurately.
Also for the record I have ran into my fair share of wild animals. I never had a problem with rattlers, bears, coyotes, etc. Most of the time these scary creatures want no parts of you and will take off as soon as they see you. I actually get excited to see them and most of the time I carefully try to snap a picture. There is no need to go blasting away at them, but its good to have a firearm for that 1% chance encounter that turns ugly.