Cats and dogs are different. Dogs have a non-domestic/wild component that is rarely seen by most people who have dogs, even though it is indisputably there.
Cats, on the other hand, have a rather large, non-domestic/wild component that almost every cat owner has seen occasionally, if not frequently.
I see very little difference between a domestic cat and nearly any large cat such as a tiger except physical size, the domestic component, and the distance to the non-domestic/wild component.
Dogs are like people in many ways.
Cats are like cats who like people.
Yes, while both can sense your mood, seemingly knowing when you're sick or feeling down, a dog will come up and try to comfort you. A cat, sensing the same, will just say, "So--I don't give a crap."
I agree completely. Years ago I read a book called The Tiger On Your Couch (or something like that) which put forth the exact same idea.