hang-up vs obstacle

hang-up and obstacle both are nouns.

Word	Noun	Adjective	Verb	Adverb
hang-up	Yes	No	No	No
obstacle	Yes	No	No	No

As nouns, obstacle is a hypernym of hang-up; that is, obstacle is a word with a broader meaning than hang-up:

hang-up: an unforeseen obstacle
obstacle: something immaterial that stands in the way and must be circumvented or surmounted

Other hypernyms of hang-up include obstruction.

hang-up (noun)	obstacle (noun)
an unforeseen obstacle	an obstruction that stands in the way (and must be removed or surmounted or circumvented)
an emotional preoccupation	something immaterial that stands in the way and must be circumvented or surmounted