In what ways were the Soviets more successful than NATO in fighting the Afghan insurgency?
It's hard to find ways in which the Soviets were, in fact more successful than NATO and the United States in fighting the protracted counterinsurgency in Afghanistan.
One might argue that they had fewer restrictions and virtually no rules of engagement so that they were free to pursue whatever tactics they wished or felt were successful as opposed to considering the impact on civilians or the popularity of the insurgency or the government, but in insurgencies, those two principles cannot be divorced. The attitude of the population towards the invading and occupying army and the strength of the insurgency are intimately connected.
Rather than attempt to pacify a province, the Red Army would more often simply attempt to depopulate it. Their brutality made the inability to control the countryside and weak support of the communist government of Afghanistan inevitable.
The one area I would argue they were more successful is in their use of helicopters. The "Hind" Mi-24 helicopters they used were extremely well suited to the terrain, were well armored and armed, and at times seemed to bring the Soviets to the edge of victory. Without American aid and missiles, it might still have been possible.