The Euro's current problems are due to governments with Euro-denominated debt being unable to take the easy way out of servicing their debt by printing money. One of Bitcoin's defining features is that it's impossible for governments to devalue the currency by just printing money.
Since both currencies behave the same way in this regard, a Bitcoin economy would feature the exact same Achilles heel that is causing such trouble for the Eurozone right now.
The problem for a country like, for instance Spain, is that their current account balance has gone highly negative. This can be due to government overspending or private overspending and contraction.
In fact Spain didn't have a big public debt problem before the crisis. Their problems stem mostly from contraction of the private sector.
If Spain had its own currency, the current account deficit would create a surplus of peseta on the international markets and drive up the price of imports for Spain, while making products produced in Spain cheaper and easier to export. Devaluation would cause short term pain as Spaniards find themselves unable to afford foreign goods but long term prosperity as it would allow their economy to require its footing through favorable export terms.
The Euro itself won't be devalued as long as Germany retains a current account surplus. Ironically a very substantial part of Germany's surplus is exports to the so-called "PIIGS."
In the US we have examples of winner and loser regions due to our common currency. Witness: Michigan vs. Georgia. The situation here is different though because money can still flow into a loser state like Michigan through the federal government (social security payments, for instance, and highway funds). And most importantly Americans are highly mobile; Michiganders can head off to Chicago or Atlanta so while the prospects for Michigan itself remain bleak, people aren't trapped.
The people in the "PIIGS" countries are facing a truly bleak future. The Euro system has denied their countries the tools needed to recover on their own. And the practical realities of (the lack of) labor mobility in the Euro zone mean the people are trapped.
Spain not only didn't have a public debt problem, it was running a surplus on a debt of 60%. And Spain understood the risk of the asset bubble and tried to stop bad property lending by reforming its banks - no help at all, since German banks stepped in to provide inadequately covered loans to finance the bubble... Now PIIGS countries must not default so that foolish non-PIIGS banks don't have their balance sheets destroyed.
The simple morality tale that many try to weave does not survive a closer look at events.
While I agree with your characterisation of the problem, devaluation is no panacea since (i) it tends to cause inflation, (ii) it only works as advertised if there is adequate global demand, and (iii) the devaluation is equivalent to a default from the point of view of creditors. I lean towards some sort of Eurobond supported by an intra-Eurozone investment programme to support trade imbalances.
Finally PIIGS is an awful acronym, who came up with it? PIGIS would be much better, and could be pronounced "piggies".
Hmm, don't Spaniards legally have the same ability to move to Germany to take work on equal terms with Germans? What prevents this from happening in practice? Language barrier, prejudice, or ... ?
For longer periods, you need a visa or a work permit (but it is usually much simpler to obtain if you come from the Schengen area).
http://ec.europa.eu/youreurope/citizens/work/migrant-worker/...
In addition, any EU citizen is free to work in any EU member country with no restrictions. For example, as a UK citizen I can choose to work in Germany without needing a visa, despite the UK being outside the Schengen Area.
http://en.wikipedia.org/wiki/Freedom_of_movement_for_workers
So... Bad for them (governments), bad for their foolish creditors but a matter of trifling importance for bitcoin as protocol and store of value.