neck of the woods vs neighborhood

neck of the woods and neighborhood both are nouns.

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

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

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

neck of the woods (noun)	neighborhood (noun)
a surrounding or nearby region	people living near one another
	a surrounding or nearby region
	an area within a city or town that has some distinctive features (especially one forming a community)
	the approximate amount of something (usually used prepositionally as in `in the region of')