This thread, like any of the others about dogs, is doomed to a lock. Folks just can't seem to remain civil and on topic, even though it can be a worthwhile topic.
That being said I have dispatched exactly one 'pitbull' who had turned calf killer and cow mauler along with what was likely a litter mate. One got away clean. The other I plugged with a .22 Stinger in the heart lung area from a Marlin rifle at about 25 yards or less. She took off like greased lightning for about another 25 yards kind of listing to one side, and then flopped down dead as dirt. I would usually use a larger weapon, but there was a reason at that place and time to be concerned about something bigger flying through a dog and ending up where I didn't want it. I myself have a 24" at the shoulder American Bulldog and a half grown American Staffordshire Terrier mix that is currently 14" and getting thicker by the day almost. Both are wonderful family dogs. We have lots of room inside and out, and I am not without dog experience. They are not dogs for first time owners, too active and strong willed. If my big one wanted to put the hurt on a guy you better be fast and good. He is fully powerful enough to drag a man down who is unsuspecting. Working dogs are simply not bred to be human aggressive. It is taught, or inappropriately bred. I do not count protectiveness as aggressiveness. Long story short, I killed one with a small caliber and killed it effectively. I used a small caliber for a reason, and would have used something larger otherwise. I have had to dispatch other dogs and think a .22 Mag is pretty effective out of a rifle. .357s or something starting with a 4 would be my choice if given a choice for an aggressive one. Almost any center fire rifle would do the deed just fine.
Couldn't have expressed it any better. Pits and Am Staffs make for great family dogs. I had two American Staffordshires, male and female, best dogs I ever had, probably won't ever have something that friendly, kind, loving, and faithful. Bring them up properly, love them, be their leader, and you'll have the perfect dog. I have decided not to have any more of these dogs because we have Breed Specific Legislation over here and it's a pain. They have to wear a muzzle, and you can't let them free anywhere.
I have never had to shoot a dog, but I've been close. Didn't happen on duty, but some time I went for a run and passed by a fence. Inside was this gigantic mastiff, big enough to jump the fence and make a snack of my poor a*s. I wasn't carrying at that time and to be honest, didn't consider to carry when going jogging. I just learnt to avoid that kind of encounters by using alternate routes.
Different story was in one of my former peakeeping tours. I lived in an area which was known for having rabies-infested animals, and you can't take chances with that. My pistols was always with me and ready to go. Happily enough, I never had to use it.