price of admission vs admission fee

price of admission and admission fee both are nouns.

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

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

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

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