The US has probably greater fiscal transfers between states and the federal budget is bigger than the EU budget compared to the member states' budgets.
Euro countries are supposed to do that too, it's part of the deal. Not everyone cares too much about that, though. It's easier to be yelled at by the ECB than your voters when the latter will vote you out of office.
The big difference is that flow of capital, goods, and (most importantly) labor between states is virtually unrestricted. In Europe, this isn't the case, which is a big reason Europe isn't an "optimal currency zone" (http://en.wikipedia.org/wiki/Optimum_currency_area).
What restrictions are there on labor moving between states in the EU? I'm not aware of any at all - witness the large numbers of Poles who now work in the UK (which I admit I rather like).
I don't know about legal restrictions, but I frequently see the claim that people empirically don't move within the EU as much as they move within the US. I'd guess that variability of language/culture probably plays a role...
There are no legal restrictions for most countries; recent entrants to the EU don't get full access to labor markets of most other EU countries immediately. But generally people can move or invest where they like, and EU-wide standards have been established most products and services (so your widget/widgeteria doesn't have to be approved by 22 different regulatory agencies).
There are no internal customs controls in the continental EU; the UK and Ireland reserve an exception, partly due to historical problems with terrorism.
Most states run balanced budgets most years, and some have been in surplus quite recently. Of course, they do that partly by shifting funding of state government functions to the federal budget, which is not constitutionally required to be balanced as most state budgets are.
Actually, I wrote that with the intention of disagreement, but now I think about it ...