Raw healing output: WHM
Mitigation: SCH
Raid utility: AST

In a raid setting, I would choose SCH for preemptive healing. In my experience, when raids wipe to damage in this game it's more often because it's high damage they weren't prepared for rather than high damage they simply couldn't heal through. It's safer for the raid to take 50% damage and be topped off in 2-3 globals, than to take 75% damage and be topped off in the same amount of time.

There are other reasons like minimal overhealing and the costless casters that are fairies, but that's the main one. There's also the fact that they have an absurd amount of sustained DPS for a healer, by far the highest of the three.

I would take an AST or WHM for a fight with a lot of sustained incoming damage, with preference on the AST for extra raid dps via cards. If you're really serious about healing, level all 3 and choose based on the fight.

In an instance setting, just yolo and pick whichever you enjoy the most.