Do "special" arrow types do more damage than regular arrows when their special ability does NOT directly affect the target?

Solution 1:

According to this post, all arrows do the same amount of base damage. Bomb arrows appear to do a little bit extra, though that's probably because the enemy takes damage from both the arrow itself and the resulting explosion.

Certain elemental arrows can be used to instantly kill enemies of the opposite type. Fire arrows kill ice enemies, ice arrows kill fire enemies, and ancient arrows kill Guardian enemies (if you shoot them in the eye, otherwise they always take 1/3 of their maximum health in damage). Other than that, the only benefit to using elemental arrows is to apply the elemental effect to the enemy hit.