Earlier quoted context omitted.
Dogs can be trained ( https://en.wikipedia.org/wiki/Rat_Terrier ) to kill rats in a much more controlled fashion than having free range cats wandering around.
Grew up with cats that would kill mice, but weren't very good at it. Got a miniature pinscher, which were also bred to kill rodents, and it was amazing how lethal they were around mice. Grab, bite, dead.
Mole problem? Borrow a dachshund for a week, no more moles. For efficient, methodical obliteration of a local pest population, hard to beat a canine for Terminator-like determination and efficiency. Cats just dick around too much.