If the US were organized like the EU, several of the states would be heavily indebted and bankrupt, with a third world quality of life, and the financial, industrial, and entertainment centers would be even richer. Instead, richer states transfer huge amounts of money to poorer states through various federal programs (infrastructure spending, assistance to the states, federal welfare programs, etc.), going a long way towards putting citizens on an equal footing everywhere in the nation. The banking system is unified and federally insured, disaster relief is centrally supported, people are free to move around entirely freely as citizenship is handled at the national level. Every state has a comparable seat at the political table.

The weaker states in Europe should have never agreed to a currency union without any kind of fiscal or political union. It led to a massive bubble of stupidly cheap debt and speculative capital inflow, and then when the economy started looking iffy all the money flowed out again, and poof.

Losing control of your monetary policy is straightjacket enough when your economy dips, but under the rules of their debt deals, Greece also lost control over fiscal policy, and was forced to apply pro-cyclical cuts to government spending. They ended up in worse-than-great-depression level economic collapse, with absolutely no tools available to deal with it.

For Germany by contrast, the Euro has been great (though fiscal austerity in response to a recession was stupid for them too). Their currency has been artificially weak relative to their neighbors, helping them run huge trade surpluses.