You check the base stats of the attacking owl and the target(s) during battle and subtract the defense from the attack value.
So the hero card stats and troop bonuses apply, as well as wither and grow, but any other buff or debuff is ignored.
The two formulas are stated here.
Formula for Moonrise Strike:
Moonrise Strike damage = max damage / 2000 x (attack - defense) + max damage / 2 x (1 + damage increase) (round down)
with
damage increase = owl’s increased damage % against holy, if target is holy, otherwise 0
Max damage occurs when the owl’s attack is >=1000 larger than the target’s defense.
Min damage occurs when the owl’s attack <=500 smaller than the target’s defense.
Formula for the MR Ward should be:
Moonrise Ward damage reduction = max reduction / 2000 x (attack - defense) + max reduction / 2 x (1 + reduction increase) (round down)
with
reduction increase = owl’s increased reduction % for holy, if attacker is holy, otherwise 0
Max damage reduction occurs when the attacker’s attack is >=1000 smaller than the target’s defense.
Min damage reduction occurs when the attacker’s attack <=500 larger than the target’s defense.