I have never gotten the flow for AST to get max efficiency for progression. I seem to do well with SCH though. So from what I'm understanding, WHM is best for REALLY early game and are great for level, SCH is great for leveling and can hold their own well in progression, and AST is the god of healing progression but suck for leveling due to the good actions being late game.
I have all the healers at 70 so I should play around with each at equal powered gear and such to play with the overall power of their abilities. Mostly just to experiment. I feel the most comfortable with SCH and I used to love WHM back in HW, but AST was one that I always struggled with since I find the card system is so annoying to deal with personally due to RNG being aggrevating and it never giving me what I need.