I have been reading this thread with great interest, as I just got my first class to 60 yesterday (WHM). My AST is 51. And I am truly unsure as to which class I want to focus my eventual esoterics on.

From what I've gathered, the WHM has cooldowns that allow it to push its healing beyond that of the AST, and to have a bit more DPS and mana longevity.
But the AST has this entirely additional unique Cards system, while replicating most of the WHM's AE healing toolkit. It just seems that the AST can do most of what the WHM can do, but can also explore this entirely additional Cards-based system, or switch to shields. It just seems like the AST offers more variety? It seems that the White Mage has slightly stronger AE heals, but the AST has AE heals and an entirely different realm of gameplay. When I hit Assize on my WHM, it doesn't really feel like I'm engaging a unique system, but I do get that sense when I'm flipping through Cards on my AST.