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In tabletop, Arcane Bodkins(treated as a weapon) are 30 inch range Strength 3 with -3 to armor save, while the Bow of Avelon is 24 inch range strength 4(built-in -1 to armor save) magical fire and have additional -1 to armor save against Force of Destruction.
In CTT's formula, Strength 4 does deal more damage but the AP ratio of HE sister (-2 at max) would be lower than the -3 of arcane bodkins.
So HE sister does have stronger total damage, but when against heavily armored foe (like dwarf) arcane bodkins is stronger.