Quick comparison

[Meta-Flare]

Before I start let me say I know that I am a healer and shouldn't worry that much about damage but I like to do more than sit there in those moments where no heals are needed.

Now my actual question is which healer role, scholar or whm, is the better damager? I know they both have access to cleric stance but we whm have holy and it's pretty strong even if it is a stupid point blank aoe.

[Hysterior]

In party I don't see why you would need to attack anything... you could possibly put dots but I would advise to focus on healing
SCH is terrible for solo, you would nee an attacker/tank Chocobo to help you all the time to do anything

[Eccho]

For end game being able to switch to dps is pretty important. Titan HM for instance we currently run it with 3 healers. 2 of which switch to DPS during the heart phase.
For Amdapor keep as a scholar I cleric stance and DPS the entire dungeon letting my faerie do the healing.
The WHM does do the larger focused damage. Stone two has a much higher potency than any SCH skills. however the Scholar has 2 instant cast dots and an instant cast burst + blind. The WHM Dps skills use a lot of mana and cannot be spammed for long but a SCH can more efficiently throw in a little DPS here and there during all boss fights. You will more often see SCH's using dps moves during a fight than a WHM.

[Morthis]

Solo, probably WHM. Holy is also very strong for aoeing and fate grinding.

Grouped I would go with scholar. WHM does more burst damage, but scholar retains passive healing when dpsing (faerie) and scholar generally has a lot more mp to spare. WHM damage is actually fairly mana intensive (even outside of holy, which costs a truckload of mana).