Humans are dirty, filthy creatures, always secreting some smelly chemicals as a direct or indirect (via metabolism, etc) response to stimuli and/or unusual operating parameters (illness, injury, etc).

Dogs have excellent olfactory systems, so they can pick up on the minute changes to your normal smelly self and respond as they think is necessary.

Unsurprising that a dog would pick up on stress smells and try to ensure its survival by trying to calm your ass down a little.

Cats, of course, may be able to discern your emotional state either by observation or scents, but they usually just do what they want anyway and so are not to be relied upon as a comfort animal.

/I like cats and dogs
//but cats like to walk by themselves
///and dogs have more history of being bred exclusively as working and companion animals, so they have a leg up