No clue why you would get euro from an ATM at the airport (or anywhere) since 1) the rate of exchange is determined by YOUR bank so it is a wash where you get cash. The ATM bank is just dispensing the euro and 2) with USD there are many places that discount for cash transactions in USD. If you are REQUIRED to pay for a service in euro then that is a different situation

The only ATM difference would be the charge by the ATM bank for the use of their service ($3-$7.50) and there are a lot of cards that reimburse that fee anyway

CC charges should always be in the currency of the country you are in (euro) so, again, it will be YOUR back doing the conversion and not the merchant