WHM is a powerhouse HPS-pumper that's fairly straightforward. Highest healing on demand, good bursty healing as well and they have 3 HoTs. They recently got some powerful DPS tools as well but whether they will be practical for raids or not is to be seen (accuracy issues, potential MP issues in having to keep up the healing, still not as fluid for stance-switching as a SCH).

SCH is currently in a spot where it's pretty much good at everything. Best shielding, best sustained single-target healing (and easiest on the sustainability there, too), good utility, able to DPS a lot, able to buff the party via Selene's Haste buff, etc. They used to be a bit lacking in the AoE-healing department (especially without using their healer fairy, Eos), but they now got a tool that turns some of their shields' shielded portions into pure heals, as well as an oGCD 400 potency AoE heal (on a 30s CD, costing an Aetherflow stack too). SCH also brings Supervirus.

AST... Well, we've had a lot of whining about it on the forums lately. It is supposed to be a buffer-type of healer that sacrifices some of its power in favour of versatility, mobility and being able to buff the party. However, at present many people feel like AST is underpowered due to the cards not being significant enough to warrant having such 'low' healing. Keep in mind though that their bread and butter kit is similar to that of a WHM, only without a Cure III and without being able to buff their heals in some form (like Divine Seal). I do agree AST could use some minor tweaks and buffs to some skills, but they are not in a terrible shape.

Right now, the way I see it is that a 8-man raiding group should have a SCH, with the 2nd slot being either WHM or AST.