Ingredient lists are too large to publish here. Hill's 1st 3 ingredients are Ground Whole Grain Corn, Chicken By-Product Meal and Pork Fat. Innova's 1st 3 are Chicken, Chicken Meal, Barley.
Any time a grain is listed in the first five ingredients the food is not something I would feed. Chicken by-products include intestines (and their contents) heads and feet (which are probably good protein, but sounds gross), and any and all other parts of the chicken.
Chicken Meal on the other hand is meat which has been cooked and dried and crushed into a powder. Some of you other food experts out there correct me if I am wrong, but meal can contain parts that you and I don't ordinarly eat, lungs, kidneys, hearts, and other organ meat, but it does not contain by-products.
Remember, vets aren't usually nutritionists, just as human doctors aren't. Big dog food companies spend a lot of money romancing vets to get them to sell their products. I am sure your vet made the very best recommendation from the information at hand. Good luck!
I feed Innova EVO to my three Yorkies and I doubt that I will change any time soon. 