[ahje]

EU citizens are able to move to another EU country are eligible for the same benefits as locals as long as they are working and paying taxes there and for X time after that (I can't remember the exact number).

In the Nordic countries that's extended quite a bit for citizens of other Nordic countries (even if the other country isn't in the EU), and I wouldn't be surprised if there are other groups of countries in the EU with their own similar agreements.

None of the above says anything about the level of welfare the individual EU countries have, however. If an EU member has a below-average welfare system then you might end up with nothing simply because you don't meet the requirements for receiving benefits.