There are many places in the US that have more of a problem with feral cats than rodents (which doesn't happen with dogs as much here). Some trap/neuter/release programs exist for these, but they struggle. Often the only service they provide the community - beyond simply neutering the wild cats - is a steady supply of pet kittens (also made sterile). I'm sure many people involved would love to see the wild parent cats actually made useful for something, which could also help reduce the problem of the thousands of unwanted cats that are euthanized every day.
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.
My cats kill moles and mice. They do a damn good job of it. Only thing dogs seem capable of killing: rabbits and themselves.
Umm, I think you misread my statement, which was intended as "in a contest of who catches the most rats...". It was not intended as cat vs. dog in a cage match.
Though if that's the direction you want to go, the terriers I personally have are "American Pit Bull Terriers". Tell your cat to bring its A game.