Credit cards issued in the EU can be used worldwide, costs and fees depends a lot on the country but cards with no foreign transaction fees and no currency exchange fees do exist in some countries (e.g. Fortuneo in France). Premium credit cards with additional insurance are also very much available, in some cases without any monthly fees.
Many European countries have popular debit card network that can be used locally for cashless payment but a credit card is certainly very useful, especially if you travel abroad (which is this site's main theme).
At the same time, there are many differences with the US. Very high credit limit are unusual, as is not paying your full credit card bill every month. It's not common to get multiple credit cards just for credit, cash backs are lower or non-existent.
The fraud landscape is also completely different. Disputes and protections exist, especially if your PIN wasn't used. However, chip-and-PIN is the default and fraud is much lower in the EU to begin with. In fact, fraud has become so hard that criminals actually prefer to use the cards they steal in the US! Consequently, it's often necessary to explicitly notify your bank if you want to be able to use your card in the US or without using the chip (I have had banks in two different countries with a feature like that in their app, neobanks and fintechs do it too).
Of course, whether it's worth getting another credit card if you still have access to your US credit card is a completely different question. It's going to depend a lot of where your income comes from: If you get an income in euros and have bills and expenses in a European country, you will almost certainly want a bank account and local bank card. Making sure that card is a credit card or getting an additional credit card would spare you the fees and troubles of transferring your money back to some US account.
On the other hand, if your income still comes from the US or you can pay your US credit card bills from your EU account without too much trouble then I guess getting an EU-based credit card won't make a ton of difference and probably isn't worth the trouble.