price of admission vs admission charge

price of admission and admission charge both are nouns.

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

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

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

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