There is no evidence that a normal, healthy cat or dog would be healthier on a higher-protein or grain-free diet. There is also no evidence that eating a higher-protein or grain-free diet would harm a healthy pet. Nevertheless, both are trendy marketing terms.
Keep in mind, each company may have its own definition of what constitutes “high-protein.” Also, high-protein is not necessarily grain-free and vice versa. In some instances, cats or dogs may do better on higher-protein diets, such as during weight loss and during growth; puppies and kittens need more protein than adults. However, in cats or dogs with kidney disease, higher protein can be harmful.
Nor are all proteins created equal: Each protein source, such as egg or soybean, may contain different essential nutrients. In addition, the processing methods and fiber content will determine digestibility more than the protein source itself. Focus less on the ingredients and more on the nutrients. Talk with your vet about what diet is in your pet’s best interest.