precisely vs on the nose

precisely is not an adjective while on the nose is an adjective.

Word	Noun	Adjective	Verb	Adverb
precisely	No	No	No	Yes
on the nose	No	Yes	No	Yes

As adverbs, precisely and on the nose are synonyms defined as:

Other synonyms of precisely include exactly, on the button, on the dot.

precisely (adjective)	on the nose (adjective)
	being precise with regard to a prescribed or specified criterion

precisely (adverb)	on the nose (adverb)
indicating exactness or preciseness	just as it should be
in a precise manner
just as it should be