That's generally true, but not always.I'm going to get me a six pack of outdoor cats the local shelter calls the "working cat" program. There is nothing more effective at rodent control at my house. My neighbors 2 cats work hard but they are not outside enough.
Mouse traps just don't work.
I love dogs though! Buy they don't catch and mangle mice and roof rats however. Not a problem with a cat.
We have 3 "outside" cats and 3 dogs.
Two of the three cats are too lazy to hunt, they just wait for a bowl of food. They sit outside the door and bawl if it's dinner time and nobody fed them.
Two of our dogs, one in particular, LOVES to kill mice. She follows my wife into the chicken pens every chance she gets.
Dogs have "owners", cats have "staff".