Yes, he's as bad in private as in public

That is surely the key thing to take away from the leaked Trump phone call transcripts (as well as the fact that there must be very worried people within the government in order for the leak to happen at all).  As The Guardian writes:

Such documents should have been very closely held, accessible to only a few senior officials. Their publication reflects the intensity of the war inside the White House between rival factions – and a reminder that, for all his well-advertised toughness, the new chief of staff, John Kelly, is going to find it very hard to impose discipline on an institution that is dysfunctional from the top down.

It is quite possible that the leaker was motivated by anxiety about the national security implications of Trump’s erratic leadership – that the leak is a cry for help from inside the administration.

The transcripts of his conversations with Enrique Peña Nieto and Malcolm Turnbull show the president to be no more coherent in private than he is public: ill-informed – even about a major attack on US soil – and narcissistic to the point of absurdity.