neck of the woods vs neighbourhood

neck of the woods and neighbourhood both are nouns.

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

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

Other synonyms of neck of the woods include locality, neighborhood, vicinity.

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