It is very important to note that wild cats and dogs hunt for their own food because that is their only means of survival. Domestic cats and dogs no longer need to hunt for survival because we give them the food they need.
You could feed them raw meat of animals they can naturally hunt and kill or you could allow them to hunt for themselves if you live in an area that has an abundance of the animals listed above.
With the exception of hunting dog breeds and dingos, most dogs, especially the smaller dog breeds, no longer have the ability to hunt for survival. Even if they still have the ability to hunt, they are most likely not going to hunt as a means of survival.
Domestic cats on the other hand, still have the ability to hunt but they may not always eat their prey because they do it for the thrill of hunting and might even bring back a dead bird or rodent as a present to you.