Ugo: Thanks a lot. You have it exactly right. An important footnote however:
As you say, Modigliani-Miller implies same average rate, higher marginal rate if deficit is financed through national debt.
If however the eurobonds benefit from a liquidity premium (which is the main reason for doing it), the implication is: lower average rate, relatively higher marginal rate.
If eurobonds imply a more robust Euro financial system and a lower risk of crisis, then the implication is: lower average rate, and potentially, even lower marginal rate.
But one should not oversell and be too greedy. I shall settle for the outcome in the second paragraph.