yes you are. each country still has its own passports, which are also EU passports. German/EU passport. Austrian/ EU passport etc. And nationals receive certain benefits which other EU members do not necessarily recieve. For example health insurance. So if you have a choice as to which "EU" passport to take, first look into the individual country benefits.....take advantage of the system, since the system takes advantage of you.......
U.K. is offering 4,000 resettlement spaces for Syrian refugees, UNHCR spokeswoman says (Reuters)
from the article: Fear is driving Israelis to obtain foreign passports