I think there's been a pretty thorough coverage of the healers so far, particular from SovereignAegis. I just want to round out the info with WHM a little more on 2 points:
1. WHM actually has excellent single target healing. Cure II has always been considerably more powerful than lustrate, even on tanks pre-heavensward. In fact, cure I + Divine Seal would do that.
The strength of lustrate is that it's 1. instant and 2. 1 second recast. WHM spells have significant lead time -- as another poster said, you need to be very proactive on WHM, while SCH's lustrate excels at emergency healing.
Also, just as SCH has gotten more tools to help with AoE healing, WHM has gotten a few more instant heals with the expansion to help with the whole lead time thing.
2. DPS. WHM can actually do pretty good DPS, especially with the expac now. The catch is there's no healing pet to keep up healing in the DPS stance. However, bismarck ex and ravana ex, as examples, both have burn phases without much or any damage going out. Throw out HoTs, hit cleric, and nuke away -- in this circumstance WHM does OK, and may even have advantages in certain circumstances as its damage is front loaded.
Generally, however, if you want to focus on maximizing DPS while healing, SCH is the way to go.
My AST is not 60 yet but it's DPS abilities seem to be a 1:1 copy of WHM dps skills, but with 10 less potency.
