Show of Power emulates automatic effects precisely
Page 114 of Flowers of Hell, emphasis mine:
If it is an inherent ability or Merit, the demon benefits from it until the end of the scene. Otherwise, it lasts as long as it normally would and has the same effect as if the demon's player had scored a single success on any required roll.
So, here would be the sequence of events: the player running Demon Debbie declares his intention for Debbie to mimic the damage resistant Vampire Vinnie that Debbie saw the other week. The ST looks at his notes, sees that Vinnie had Armor of Scars at 4 dots for damage mitigation, so, when Debbie's player rolls at least one success, she benefits from the 4 dot version of Armor of Scars, what she witnessed.
Later, Debbie is trying to emulate something she saw Promethean Paula do: Dopplelganger: Incriminate (PtC:2nd, page 133), wherein Paula scapegoated someone for a week (Paula rolled an Extraordinary Success, 5+ successes)
Debbie's dice hit the table again, but because she's trying to emulate an ability whose success hinges upon a dice roll (how many days the scapegoating lasts), Debbie can frame her victim for either 1 day (1 - 4 successes on Debbie's roll) or 3 days (Exceptional Success, 5+ successes on Debbie's roll.)
Basically, if no dice were needed for the original effect to transpire, the Demon can perfectly emulate it. If a roll was needed, the Demon can emulate it weakly. Armor of Scars requires no dice roll to active; so the Demon gets whatever intensity they saw.