Money transfers within the EU have to cost the same as transfers within the countries themselves, by law (for transactions smaller than 50k Euro). And we're talking mostly direct bank transfers here, not something like Western Union.
In Germany, your ATM card is basically always a direct debit card that gets accepted anywhere (causes the shops lower fees than credit cards), so that takes care of one part of the Visa/MasterCard angle, and for online transactions direct debit rules the game, taking care of the other half. Services like paypal use direct debit a lot in the background.
(So the only "missing" part is credit card debt, usually you can't accrue that much debt on your direct debit account)
As a minor correction, the EU law on fees only applies to Euro-denominated accounts. I was somewhat unpleasantly surprised that I was charged significantly higher fees when I transferred some money from a EUR account in a Eurozone country to a DKK account in Denmark, since that case doesn't fall within the regulation.
Yes, under 50k Euro and in Euro, should've said that a bit more clearer.
Those foreign currency fees can be a bit tricky, even for credit cards. I've got two MasterCards, one of them adds a 1% fee if it isn't in Euro, the other doesn't (well, I got it exactly for that reason).
In Germany, your ATM card is basically always a direct debit card that gets accepted anywhere (causes the shops lower fees than credit cards), so that takes care of one part of the Visa/MasterCard angle, and for online transactions direct debit rules the game, taking care of the other half. Services like paypal use direct debit a lot in the background.
(So the only "missing" part is credit card debt, usually you can't accrue that much debt on your direct debit account)