I doubt the barbarians were particularly gentle when looting a town; it was more that the Romans took systematic sacking to a new level. And this was just for "ordinary" opponents who did not surrender in time. The razing of Carthage is special, and there's something hysterical about Rome's hostility to Carthage in the run-up to the Third Punic War. The city was no serious threat, yet it seems the Romans were determined to find offence.
Also, it should be noted the later sacks of Rome were steeped in the politics of the dying Western Empire. Alaric and his Goths formed the mainstray of the Roman army for years. They had been promised land, yet time and again found themselves treated as second-rate citizens. They took Rome to make a political point, attempted to install a new emperor, negotiated, and only when that failed did they sack it. The Vandals had similarly been promised land and not gotten it, so they set up their own pirate empire. Their attack on Rome came at the invitation of a former empress who needed rescuing.
In both cases the attackers had tried to become part of the Roman Empire, so clearly they didn't hate it. It was the political games of the Roman generals, and their reliance on barbarian warriors as cheap firepower, that provoked the sacks. However, before this is cast as "scheming Romans" vs. "noble Barbarians", it should be noted that the Roman generals were often from barbarian ethnicities themselves. In fact: during part of this period the Western Empire was practically controlled by a Vandal, Stilicho.
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