Both. It may very well lead to some of the peripheral members to leave the eurozone and as a result give the core more strength.
The very large imbalances between the saving/exporting core and the spending/importing fringe cannot be resolved through grinding and brutal austerity programs.
Adjustments of that nature, even if initially implemented (as Greece is trying to do) will eventually collapse, both for structural reasons and because of a lack of popular support. This could be an ugly process (extreme political instability) or orderly (governments get voted out). There is no doubt in my mind that it would be much easier politically for Greece, Portugal or Ireland to devalue. Spain might not go down this route, though.
It will also be easier for the core to manage this politically. The German or French taxpayer does not want to bail out the Greek, Irish or Portuguese, who they regard as barely a notch above leeches. They would probably think good riddance.
This would restore order in what remains of the eurozone core and allow the ECB to raise rates as needed, something they cannot do now because it would kill the fragile periphery. This will translates into a stronger core. It will also allow for a smoother path towards political union, if that ideal manages to survive.
Eventually this may also turn into a benefit for the periphery, as they will be able to export to the neighboring core in much more advantageous terms and benefit from other sources of income, such as tourism and remittances, and as they move on their schedule to sort out their finances capital inflows could help the process too.
The transition will not be pretty, though. There is much money to be made in currency trading and in spread differentials during the volatile transition time. But I think eventually it will all work out.
Raul Elizalde, Path Financial LLC