dullness vs insensibility

dullness and insensibility both are nouns.

Word	Noun	Adjective	Verb	Adverb
dullness	Yes	No	No	No
insensibility	Yes	No	No	No

As nouns, insensibility is a hypernym of dullness; that is, insensibility is a word with a broader meaning than dullness:

Other hypernyms of dullness include callosity, callousness, hardness, unfeelingness.

dullness (noun)	insensibility (noun)
lack of sensibility	devoid of passion or feeling; hardheartedness
without sharpness or clearness of edge or point	a lack of sensibility
the quality of lacking interestingness
a lack of visual brightness
the quality of being slow to understand