In my experience, both US and European banks are pretty easy to access via ATMs worldwide. (That was the easy part!)
However the issue of what currency to hold (USD, Euros, etc) can be a bit tricky. Transferring all your money to Euros is a gamble, because who really knows what the exchange rates will do down the line. (sure wish I had moved all my money to Euros three years ago though!) Also, you'll likely pay some rather hefty fees to effect the conversion, depending how you go about it.
Realize, too, though, that using your US ATM card in a European ATM might cost you a 'hidden' fee in the exchange rate -- check with your bank to see what exchange rate they use. Often it's the "daily interbank rate plus x%" (1, 2, 3%, etc) -- works in similar ways with other banks and other currencies as well. While your at it, check your credit card's exchange rates - they can vary as well from bank to bank.
At any rate, ATMs and credit cards will 99.99% of the time give you much better exchange rates than credit card cash advances or 'money exchange' windows in foreign cities.
I happen to have a US and a European bank account (ABN AMRO) purely because I lived in Holland for the past three years. One benefit to having two accounts is that if I were to lose one ATM card (or simply wear it out, have it stolen or whatever) - I have a second account and card as backup to get by on. Of course if both cards are in your one wallet when it's stolen -- well, that's just bad execution.
decisions decisions... this is just a jumping off point, but I hope it helps a bit --