price of admission vs admission price

price of admission and admission price both are nouns.

Word	Noun	Adjective	Verb	Adverb
price of admission	Yes	No	No	No
admission price	Yes	No	No	No

As nouns, price of admission and admission price are synonyms defined as:

Other synonyms of price of admission include admission, admission charge, admission fee, entrance fee, entrance money.

price of admission (noun)	admission price (noun)
the fee charged for admission	the fee charged for admission