Greater New York vs urban center

Greater New York and urban center both are nouns.

Word	Noun	Adjective	Verb	Adverb
Greater New York	Yes	No	No	No
urban center	Yes	No	No	No

Greater New York (noun)	urban center (noun)
the largest city in New York State and in the United States; located in southeastern New York at the mouth of the Hudson river; a major financial and cultural center	a large and densely populated urban area; may include several independent administrative districts