crassness vs insensitivity

crassness and insensitivity both are nouns.

Word	Noun	Adjective	Verb	Adverb
crassness	Yes	No	No	No
insensitivity	Yes	No	No	No

As nouns, insensitivity is a hypernym of crassness; that is, insensitivity is a word with a broader meaning than crassness:

crassness: the quality of being crass--devoid of refinement
insensitivity: the inability to respond to affective changes in your interpersonal environment

Other hypernyms of crassness include insensitiveness.

crassness (noun)	insensitivity (noun)
the quality of being crass--devoid of refinement	the inability to respond to affective changes in your interpersonal environment