Honestly I feel like each healer actually heals fine. I've played WHM and AST both in every Savage and I didn't feel at a disadvantage at all in either case, I actually felt like AST heals were built better for a raid environment while WHM is better at unplanned healing.

The main difference really is how much is healer has to juggle in-between healing. WHM just has to DPS. AST is expected to DPS, while managing a card system in-between casts and not clipping and for a controller player like me, scrolling through the party list to find the right DPS to throw the card on. It's too much work.
For me it's not that AST is weak, it's simply too hectic to play efficiently enough when I can just grab WHM and DPS normally or SCH and be....well almost perfect.