The reason why I really dig the adaptation choice made in the italian dub is that up to that point Light thought of himself as Kira, a full fledged god, wearing the mask of a normal human. Light Yagami was nothing more than a facade for him.
The very moment they find out he is the actual culprit everything turns upside down: the investigation team finds out that he was actually Kira, meanwhile he finds out that he had been Light Yagami the human all along, a puny man with an inflated ego that tried to trick the world and himself into thinking he was a true deity.
The fact that he first starts crying shows his breakdown, the moment he realizes the truth himself. The laughter is nothing more than a new facade, this time however it isn't for tricking the others but himself.
To not accept the simple truth.
He is no god.
He is no Kira.
He is a failure.
The other dubs however make him have either a mental break down (the ones where he laughs in a psychothic way) or go in full denial mode (the more conservative laughs). In both cases it comes off as less strong minded or intelligent than the one in the italian adaptation, because Light is a pretty amazing MC, so showing unyeilding strength despite an epic fail comes off as a childish reaction.
Just my 2 cents anyway.