So, the same problem that the poor(er) states in the US have. And yet, they seem to be content to stay within the union - so I think there may be a little more to it than a single variable? I'm open to the argument, it just seems a little... well, short. Especially in a reply to a comment that said "The problems are more complex" :-) (now it's simple after all? I doubt it)
Those figures do not show massive inter-regional financing. All but 2 countries have net EU expenditures of +/- 250 Euro per person. Per capita spending by the EU is 215 Euro per person compared to federal government spending of $9,961 per person in the US.
The EU budget is 1% of GDP while the US federal budget is 20% GDP, 60% of which goes on social security / medicare / safety net programs. US federal spending acts as a huge inter-regional stabilizer.
Regional transfers must significantly increase within the Eurozone if the Euro is to avoid breaking up or immiserating huge numbers of citizens.