The one element is a joint supervision working according to strong unified rules. And the other element is a liquidation regime, with which Banks can be liquidated.
Personally, I have lost trust in any ability of any European institution to be able to regulate or even, for that matter, understand banking, at all. We had more than enough outright silly attempts to "stress test" the banking system. The Bundesbank itself along with the BaFin failed to investigate alleged concealed losses at the Deutsche Bank until after the SEC got involved.
What is more, is that without outside money it will be impossible to break the vicious circle of bank failures -> the state having to "rescue" the banks -> leading to increased state debt -> reduced rating -> bank failure. This can only be broken if outside money is used either by tapping the ESM or an FDIC like Euro area wide deposit insurance.
Of course we need to be able to liquidate failed banks. But the whole point of an actual banking union is to reduce the adverse local effects, by broadening the base, in case a bank fails. It should have become clear by now, that we need a risk sharing system if the want the Euro to succeed. Our choices cannot even be described as binary. We will become an optimum currency area, all we can decide is if it will be with or without the Euro. If we cannot even do the first step and introduce an actual banking union, but rather decide to change the definition of such an institution, then the Euro has no future.
Unemployment remains the most challenging issue facing the Euro area. We will also need a burden sharing mechanism in this area. A central banker, who does not even mention unemployment and makes up new definitions for banking unions, might be true to his ordo-liberal principles but in my opinion, he will in the end be nothing more than a nail in the coffin of the Euro. Or to use his own words (probably an attempt to be humorous):
Ja, ich weiß nicht, ob wirklich das Bankensystem auf den Cook-Islands am Ende sicherer ist als das Bankensystem im Euroraum.Update: of course Weidmann not mentioning unemployment might be due to him only caring about the ECB mandate, of keeping inflation just below 2 %. But that does not really makes sense, since the ECB seems to have given up their primary goal for now.
Yes, I do not know if the banking system of the Cook-Island will in the end be really safer than the banking system in the Euro area.