Intelligence is a sliding scale; there are certainly animals who are smarter than cats or dogs. In terms of what separates humans from animals, there might be fewer things than you might think. Animals have been shown to make and use tools. Dolphins and chimps can understand complex instructions once they have been taught enough words. Chimps can even learn to sign.
Animals certainly have musical ability; there's an obvious reason the term "songbirds" exists. Some birds perform mating dances. Beavers engineer and build dams. Male weaverbirds attract females by building elaborate nests (architecture!).
One thing we have that animals don't is stories. Animals have been taught to paint, but no one has yet put forward a story by a non-human. It might be because they are more honest. What is fiction, after all, but untruth? People make up stories. Animals don't.
So if you're a fiction writer, pat your dog on the head and yourself on the back. You might not be better, but you are sure as heck different.