If you live in a European Union country and move to another, is there any reason to change your citizenship?

EU citizens only have the right to stay in another country if they are employed, in full time study or are self sufficient (ie are able to support themselves without the need of state benefits). If you’re employed then you are usually eligible for the same social benefits as locals. EU citizens that are in employment are eligible for NHS treatment in the UK. Similarly, EU citizens in employment in another EU country are entitled to healthcare on the same terms as local citizens. EU citizens resident in the UK can vote in European and local elections but not in UK Parliamentary general elections and I would imagine (but don’t know for sure) that similar rules apply in other EU countries. (Also, to complicate things, in the UK citizens from Commonwealth countries resident in the UK_can_ vote in UK Parliamentary general elections.) You also don’t technically need a passport to travel between EU countries although you do need a national photographic ID card – which means if your British you need a passport because we’ve never really gone in for the whole national ID card thing.

So… short answer if you’re in employment or full time study then no there’s no real need to change your citizenship.

I recently found out that if I don’t take out Norwegian citizenship, I won’t qualify for the minimum coverage of pension. My Lithuanian friend is in the same situation. I don’t know if that is unique to Norway because it is only in the EEU and not a proper member of the EU.

A possible disadvantage is sometimes you have to give up your previous citizenship. I think, in the case of my EU citizenship, I can get another EU passport only if my country and the other country reciprocate allowing new citizens to keep their old passport – which is surprisingly unusual. In general, I would lose my citizenship if I naturalized somewhere else (though exceptions can be made when asking permission) in the EU or out.

As for the requirements, they would be national. Unlike U.S. citizenship, the status of EU citizenship is supervenient on national citizesnhip. There are common standards, but each country can make its own rules. With respect to visas, people may not be able to travel too much beyond their host their host country, though they are allowed to leave for short periods. The EU is trying to offer “blue cards” that are analogous to green cards. Not sure it’s going well, maybe because it requires national approval, but it would be analogous to green cards.

Re what @Lightlyseared said: I think they can send you back to your home country if you become indigent, but that doesn’t necessarily mean they will. I presume people have the basic rights to things like unemployment insurance and social services.

If you have your own money to pay your life you can settle within the EU… if you work and lose your job you will get the same support as locals. There is a EU-Citizenship with the Lisboa-Contract: You are allowed to vote in the communals and EU-elections.
I was born in Düsseldorf, DE and now live on Formentera island, ES, voting the communal and european elections here, the ‘Bundestag’ in Germany.
The member states still have in the meaning of statal support with unemployment some restrictions, but if I would be here without work, spain will pay my the same amount like to any spanish coworker without employment. I pay here to the ‘seguridad social’, so I will receive with my retirement money from Spain and Germany (percentage depending on who long I worked in each state). It is still not as free as in the US, but we are on a good way… our union is still a union of national states, countries… but we are on the way…