The evolution of the domestic dog has resulted in most of the breeds that humans have engineered do not have the "tear apart and eat" instinct--domestic dogs when they become strays are scavengers--they are found near garbage dumps, etc., not generally hunting and killing other animals. Although dogs, wolves, and coyotes have 78 chromosomes, dogs differ from the wild canids in that dogs have 76 autosomonal and 2 sexual chromosomes, foxes only have 72 chromosomes.
Some breeds will chase down and kill animals, but rarely will they rip the carcass apart and eat it. This is what sets domestic dogs apart from wild canids. Some domestic breeds will shake and kill, but they will not eat what they have killed. I have a book somewhere that was written by a biologist who studied these traits in dogs. It is a very interesting read. I just don't know which box it is in. I do know that one of my Saints would climb a tree, shake the branch until the fledgling robins fell out. She would squeak them to death. She never ate them, however. Ironically, she is fine around the chickens (mind you, her tree-climbing days are long behind her--she will not be with us much longer). I picked up a stray dog on the road once--she weighed 35 lb, When she died 12 years later, she weighed 68 lb. She obviously had been wandering for some time and was starving. The vet was surprised that she did not have internal organ damage. She could run like the wind, catch a frisbee on the fly, but she never caught any animals and, most likely, would never have torn them open to eat them. I had a dog once that caught and killed a rabbit. She didn't eat it. My father's hunting dog used to catch partridges and bring them to my dad--who would then have to either kill them or release them. Cats have the instinct to eat what they kill--most domestic dogs do not.
