sensibility vs sensory faculty

sensibility and sensory faculty both are nouns.

Word	Noun	Adjective	Verb	Adverb
sensibility	Yes	No	No	No
sensory faculty	Yes	No	No	No

As nouns, sensory faculty is a hypernym of sensibility; that is, sensory faculty is a word with a broader meaning than sensibility:

sensibility: (physiology) responsiveness to external stimuli; the faculty of sensation
sensory faculty: the faculty through which the external world is apprehended

Other hypernyms of sensibility include sensation, sense, sentience, sentiency.

sensibility (noun)	sensory faculty (noun)
mental responsiveness and awareness	the faculty through which the external world is apprehended
(physiology) responsiveness to external stimuli; the faculty of sensation
refined sensitivity to pleasurable or painful impressions