I use quick and dirty dicepools for NPCs generally. 2-4 dice for something they suck at, 4-6 dice for something they're kinda good at, and 6-8 dice for something they're really good at.

For conflicts entirely between NPCs, I'm liable not to roll anything and just narrate what serves the story best. If I don't know what will serve the story best, then I'll likely roll things and offer Players the opportunity to throw in positive or negative dice modifiers based on things their characters do to support one NPC over another (throwing a rock, shouting encouragement or insults, etc).