ASTs do better on average because they have better sustained healing output. WHM are still on top for raw healing with regens, SCH still have better shield abilities, but in terms of letting heal over time work their magic, AST beats them both due to stacking abilities in this specific scenario.
ASTs can both shield and stack regens - and Regens are known to be more effective in potency. However, they are hit heavier with a death because both regens and shields are weaker, which causes them to raw heal to make up for the loss when incoming damage is greater than what the regens can keep up. The problem is that ASTs lack mana sustainability compared to the other two so this problem is magnified significantly on death. Most of the times however, ASTs will not be dying as content is very easy or they are forced to learn content to use Earthly Star properly.
With pure raw healing and some regens, WHM has answers for a lot of mistakes. SCH naturally has answers to mistakes even if they don't have as potent as WHM in heals because shields add a pure HP buffer. ASTs have an answer for both but to a lesser extent. However, on a more general level - when players are playing optimally and doing mechanics, a lot of damage can be neglected - which means a lot of pure raw healing isn't needed. Damage doesn't happen as frequent so what this translates to is that ASTs are more streamlined to fit encounter design moreso than the other two by enabling regens to work.
They also have a lot of flexibility and variability with the card system - giving them a lot of things to do to support the team - at the same time they have a lot of weaving to do within A GCD window so they're constantly busy.
Basically, ASTs have a better average floor to adjust but a higher skill ceiling than the other two. This is also due to the ShB nerfs to healer kits overall. ASTs were technically supposed to be on the weaker side, but they were nerfed to the point where it becomes very difficult to play at the start of ShB since their HoTs/Shields aren't good enough that they had to be buffed to compensate. They were also buffed because a lot of people dislike the card system currently to the point lots of people still wouldn't play AST based on loss of identity.