As an ex-pat also from the US, I'll pitch in my 0,02 € :

US credit cards have the unique benefit of lush rewards and benefits that practically no one else in the world has. Without going into too much details, don't expect much out of European based banks for credit cards (usually just a deferred debit, as the balance is deducted from your bank account at period-end).

But it's still good to have a local credit card for online purchases. In my experience, US credit cards won't work on certain merchant websites even if it's Mastercard/Visa, and when you earn in local currency it's just less hassle to not have to transfer funds/convert to pay bills in USD.