I live in fear of a cat lingering too long in my garden.
I have two terriers, one of which has a very high prey drive, and they will chase anything that runs. We have a dead rat left in the garden for us about once a month, she used to get rabbits regularly (although now seems to find them dull and doesn't much bother), has caught frogs and a lizard, whch have appeared unharmed, and even managed to kill a hedgehog.
Once she's caught something, if the other dog's around he joins in, they grab a bit each and tug, just like they do with toys indoors. I have witnessed the most unedifying spectacle of them playing tug of war with a slowworm. They are impossible to stop at this point, it's like some sort of frenzy comes over them.
I don't think a cat would stand a chance with the pair of them. They're wire coated and traditionally have the fur left longer round the face to protect them, so a cat would be likely to get just a claw full of fur if it lashed out. If it was just the one dog, the cat might stand a chance, but not with the two of them. The bitch is incredibly fast, too, and can jump high, making it hard for a cat to escape the garden. Next door have a very cocky ginger cat who sauntered slowly across the lawn one day, not realising the dogs were out. If his tail had been an inch or two longer, I don't think he'd have made it over the hedge before she grabbed it. I haven't seen him in the garden since!
We used to have cats ourselves, and the last cat was ok with just the one dog, but we had to rehome him when we got the second. I've never been able to train it out of them.
I also know a woman who claims that one of her German wire-haired pointers was a cat killer, although I'm a bit sceptical about that as gun dogs aren't generally that way inclined.