neighbourhood vs neck of the woods

neighbourhood and neck of the woods both are nouns.

Word	Noun	Adjective	Verb	Adverb
neighbourhood	Yes	No	No	No
neck of the woods	Yes	No	No	No

As nouns, neighbourhood and neck of the woods are synonyms defined as:

Other synonyms of neighbourhood include locality, neighborhood, vicinity.

neighbourhood (noun)	neck of the woods (noun)
people living near one another	a surrounding or nearby region
a surrounding or nearby region