Sch's identity is not the shields(Not anymore since there are three healers for two positions in party), but your fairy and your aetherflow abilities( increasing sch's flexibility to dps and dealing with emergencies).

AST's cards are nice to play with, but in real life, lets just face the reality that whm can bring more dps to the party no matter how lucky AST are in every single each draw they have.

Overall, Sch and Nocturnal AST have different tool kit but overall they both can do the mitigation job nicely(assistant healer), I don't think anyone is superior to the other.