Alright, adding on my previous post Link.
Now that I have gotten my Scholar to 60, and I have done Alexander (Savage) on both AST and SCH (cleared on SCH) I can give you a better review.
Before anything else, I healed Savage A1 just fine on my AST, but the WHM had to work much more than compared to when I was on SCH.
To no surprise the DPS and Solo-Healing on SCH was better than on AST. Having 9 Energy Drains at the beginning is just too good. I did around 650 DPS on Scholar, while on AST I did around 500 DPS.
Generally AST and SCH have the same potency on their heals, but what makes SCH excel are the way stronger abilities they have.
Cards:
The cards AST has are all meh, even if you have "perfect" card buffs, they barely make any difference. In the Faust fight a SCH does more DPS than an AST with extended Balance/Arrow cards.
Also Bole is bad because you have to use it instead of other cards while Scholars get a free AoE Bole, aka Sacred Soil.
Celestial Opposition and Time Dilation:
Two abilities to make cards slightly better, but still don't make up for the DPS loss.
CO can be used for other abilities like Lightspeed and Luminous, but SCH has way better MP management anyway.
Collective Unconsciousness:
The shied is very situational, and there is a single use for it in the whole A1 fight, but I didn't even bother to use it, because pre-casting a heal had a bigger effect than 10% damage reduction.
Disable:
Cheap Virus knock-off that actually would stack with Virus, but also only works for a single hit. While useful it gives AST nothing that SCH couldn't do better.
Essential Dignity:
It's basically the same as Lustrate, and therefor is probably the only skill that's on par with SCH. Even though being able to cast 3 Lustrates in row has his own uses.
Now about the Abilities AST doesn't have, that SCH does.
Fairy:
A 300 single target cure that costs no MP and can be used while DPSing, dodging, healing other targets, etc.
Then you also get a free AoE Regen and Magic damage reduction with Eos, which in A1 (Savage) is really good.
Eye for an Eye, Virus and Sacred Soil:
SCH have a huge AoE shield, that can be casted from far away, and you can still use skills while it's up. As I said Virus is a "better" version than Disable, though both stack. Eye for an Eye (possibly) adds an additional 10% damage reduction that AST doesn't have.
That's 35(55)% damage reduction (vs magic) for 10 seconds that a SCH can do, compared to the 10% AST can do for a single attack.
Indomitability:
SCH get a free instant cast medica you can use every 30 seconds.
Deployment Tactics:
With this skill you can possibly give your whole raid a 8000 damage shield. Remember that time when Opressor jumps into the air and does the big AoE damage? I had multiple times where the party would literally take 0 damage just by using this skill.
Now if you just compare the damage reduction, AST is complete garbage, but the saddest part is, that AST is also worse at healing in general.
And as mentioned before, the utility cards add is being outshined by the SCH dps capabilities.
TL;DR: Comparing Nocturnal AST with SCH is like comparing Lancer with Dragoon.