The cat is haughtily independent and ignores not only orders but even suggestions. The cat will tell you exactly where to go. The dog will happily go there with you. Any relationship with a cat is conducted strictly on the cat's terms, whereas the dog is overjoyed if you so much as yawn in its direction. Dogs have owners.
Cats have staff.
Cats are arrogant, aloof, and shamelessly and transparently manipulative. They are also agile, nimble and sleek. So of course you want cats in your backfield, on both sides of the ball. I'm on him like milk on whiskers. Dogs are loyal and steadfast and uncommonly patient and quite willing to be used.