place of birth vs birthplace

place of birth and birthplace both are nouns.

Word	Noun	Adjective	Verb	Adverb
place of birth	Yes	No	No	No
birthplace	Yes	No	No	No

As nouns, place of birth and birthplace are synonyms defined as:

place of birth (noun)	birthplace (noun)
the place where someone was born	the place where someone was born
	where something originated or was nurtured in its early existence