heard that the exchange is different at the airport than at a local bank from home, is that true?

The best price for buying any currency will be in the country where that currency is used, so your rate for Euros will be better in Europe. It can vary among banks and excange booths, but will almost certainly be better at any of those establishments than you could get buying Euros outside the Eurozone.

Buying dollars, you do better in the U.S., of course.

Comparing your hometown bank to an airport in the same country, you'll have to ask. Call both on the same day and see what they tell you (remember to ask if there is a per-transaction fee).

Hmmm... which airport do you mean? Your departure one or your arrival one in Europe?

There is really no need to get euros before leaving home. Take a few hundred dollars (US) in cash with you for an emergency in Europe and to have on hand when you arrive back in the US. Rates at exchange bureaus anywhere are terrible. Get cash in the local currency from ATMs while you're in Europe. There are some important things to do BEFORE leaving home to make sure both your ATM card and your credit card will work in Europe. Here's the URL for a very helpful article that tells all you need to know about changing money in Europe: www.ricksteves.com/plan/tips/moneytip.htm.