If either The Heretic or Witch Hunt was resolved aggressively, the player character will receive the title of Inquisitor and the perk Inquisitor of Atom as rewards. If both quests were resolved peacefully, were failed, or avoided altogether, the player character will instead receive the title of Crusader and the perk Crusader of Atom instead. Both perks have the same effects, and the difference is merely how some NPCs address the Sole Survivor.
The perk provides a bonus to weapon damage. For every 100 Rads, damage is increased by 10%. Additionally, starting at 900 Rads, the damage is increased by a total of 100%.
The bonus damage applies to ballistic damage, energy damage and pure radiation damage only and does not affect explosive damage and radiation poisoning damage. In this sense, it is exactly like Bloody Mess.