Are pet foods that are cruelty free better and healthier than pet foods that aren’t?

I think you're confused. The "cruelty free" designation for pet food just means that they don't engage in any testing on laboratory animals. They aren't any better for the environment, and it means absolutely nothing in terms of how healthy the food is for your pet. There a wide range of foods and qualities that claim to be "cruelty free". 

If you're erroneously using it as a term for vegan foods, no, they definitely aren't healthier than meat-based foods for cats and dogs, which are both carnivores. 

Just because a dog food states they are cruelty free, it does not have anything to do with how healthy it is for your dog.