I think they will be big, very big.
As the world moves to supra-national powers, I see a great future for .eu and the upcoming .asia.
A .eu domain will get instant credibility as all EU government domains will move from .eu.int to .eu the coming months (no .com, .gov difference)
A nation cannot just join the EU, it's an elite club that sets strict rules.
I think .eu will be the elite among the TLD's.