Does it have such a premium? Having an EU passport works preeeetty well too.
For instance many EU countries embassies will give aid to the members of other EU states that do not have local representation.
One of the most important things embassies do is to give aid to citizens of their countries charged with crimes abroad.
That's actually part of EU law. As an EU citizen, if you have no national diplomatic or consular representation in the country you're in you're entitled to help from any other EU member's embassy or consulate.
So let's say you're a Slovakian citizen in Sierra Leone, the EU consular protection site will direct you towards the British High Commission in Freetown: http://ec.europa.eu/consularprotection/representations_en?f%...
Not sure if "powerful" is the right word either. It's more of a list of the best passports to have if you want to go on holidays. "Doesn't require a visa" usually means those countries don't require visas for short non-business trips (anything from 14 days to 6 months). E.g. you can visit the US with a German passport for 3 months for a holiday but it's extremely difficult to get a visa to move there indefinitely.
You do realise that works the same way for everybody and US visa-free entry is not a residence permit right? For instance as a US citizen you'd get visa-free entry to Iceland or Japan or New Zealand but can only stay for 90 days.
Things get a lot more difficult if you have for example an Egyptian passport.