We certainly can't tell because of the nature of the healing requirements is still unknown. Same for raid context. And potencies are not fixed.
If you want, on pure theory and if we just look at healing, a WHM could spam Cure III, Assize, Asylum, Regen and Medica II without getting in any trouble MP-wise. White mage is a cure bomb, it's not something that is to be proved.
However,
In a raid context (movement, DPS checks, efficiency of healing kit) AST and SCH can satisfy the healing requirements too.
Now if we consider the info we have now (that is likely to change, let's not forget that), I'm not sure AST and SCH are that far behind?
AST has lost its healing buff of sects but all its GCD heals have been buffed.
Earthly Star is still a powerfull free heal every minute. Collective Unconscious still has a strong regen and mitigation.
Horoscope is a nice "Plenary Indulgence" top off if one GCD heal is not enough.
Synastry is still there (although slightly nerfed, but the base GCD heal is buffed so I guess it's not a big difference).
Celestial Opposition is now a new free heal.
Celestial intersection is likely to be situational, but it's on a 30seconds CD so it's a nice free oGCD.
Neutral Sect is a heal burst tool, although based on GCD, is heals, regens and shields. It's quite powerful.
We have two charges of Essential Dignity (which is arguably one of the best healing ability in the game due to its crazy potency and short recast timer).
For MP management, we have Lucid Dreaming more frequently (20seconds of MP regen every minute) and Lightspeed that got a shorter recast time.
If anything, AST will be more about optimized offGCD healing and planned healing rather than reactive healing.
I am less familiar with SCH, but from what I see it's healing kit is quite powerful because it has so much offGCD healing abilities (Aetherflow or Fairy) and they seem quite good in terms of healing potency (Indom, Excog, butterfly fair thing, adding a regen on Sacred Soil etc.)
On the other side, WHM has a free GCD heal every 30 seconds (single target or AOE) thanks to Solace or Rapture. But Rapture (300 potency) is less interesting than Assize (400 potency+ damage+MP regen+less agro) for instance. Yes it still has powerful GCD heals too, but the real healing to consider is the one required by an encounter, not the potential healing output.
I'll repeat it, we are still unsure about potency and healing requirements so my post is just assumptions![]()