sorrowfulness vs unhappiness

sorrowfulness and unhappiness both are nouns.

Word	Noun	Adjective	Verb	Adverb
sorrowfulness	Yes	No	No	No
unhappiness	Yes	No	No	No

As nouns, unhappiness is a hypernym of sorrowfulness; that is, unhappiness is a word with a broader meaning than sorrowfulness:

sorrowfulness: the state of being sad
unhappiness: state characterized by emotions ranging from mild discontentment to deep grief

sorrowfulness (noun)	unhappiness (noun)
a state of gloomy sorrow	emotions experienced when not in a state of well-being
the state of being sad	state characterized by emotions ranging from mild discontentment to deep grief