Cats with their stealth and climbing abilities are much more efficient at hunting small animals and birds, dogs are a bit more clumsy at hunting solo and have really evolved to be at their most efficient at hunting and running down larger animals in packs.
Of course this is a bit of a generalisation and there are of course exceptions.
Many a Shetland sheepdog and various small terriers are brilliant mouse and rat catchers, the shelties I had Shep and Monty both had amazing patience and would wait days laying perfectly still waiting to ambush and pounce on a mouse.
I had a kelpie/border collie X, Jessie was an excellent instinctive snake catcher, she just knew how to handle them, I was always worried that she'd get bitten but she never did, and lived a long life, the strange thing is that she never showed any interest in hurting other animals she just hated snakes. She would play at chasing the swallows around the dam for hours on end, but that was just a game to her, she never got close to catching one, however she would steal eggs from the chooks! but never chased them.
She used to herd the cattle but after a few kicks she gave them a fairly wide berth and only helped working them at a distance she left the serious cattle working duties to the bigger dogs.
