Dogs are, generally, more loyal than cats. There is far more independance in cats and more of an assumption of ownership. What I mean is: cats sort of assume they own your house. It is in their nature. A cat assumes it is your friend; a dog assumes it is your friend and obediant underling. Dogs usually show more affection, but cats are capable of a lot of affection as well.
They are equal, but different types of pets.