There are three healing ACs (advance classes) in the game per faction. They are Operative, Sorcerer, and Mercenary on the Empire, and Scoundrel, Sage, and Commando on Republic. If you are unfamiliar with the process, you start the game as a class (i.e. Jedi Consular). At level 10, you pick an advance class (i.e. Sage), and you put talent points into one of three trees (i.e. Seer).
You can see all the talent trees here: http://www.torhead.com/skill-calc
Overall, if I had to rank the healers: Sorcerers > Operatives > Mercenaries. Note, for brevity, I will be using the Empire names for classes and abilities. If you want to play Republic, don't worry, it's the same. You'll just need to cross-check the names of the abilities. They are rapidly improving all the classes, so I expect by release, the gap between the healers will be much smaller.
Operative / Scoundrel
Base Class: Imperial Agent / Smuggler
Healing Talent Tree: Medicine / Sawbones
Closest WoW Equivalent: Holy Paladin (has mechanics reminiscent of holy power)
Equipment: Medium Armor
Primary Stat: Cunning
Unique Mechanic: "Tactical Advantage"
Talent Trees: Operatives (and Scoundrels) are the Frankensteins of healers. If you took the healing abilities of a paladin and gave them to a rogue, but left some medium-ranged attacks for good measure, you would have an operative. Two of the talent trees emphasis stealth-based melee dps, while the third talent tree is focused on healing.
Resource: Operatives use ENERGY for their resource, which is functionally identical to the bounty hunter's heat and trooper's ammo. So both sets of classes are restrained by a limited resource pool. Energy regenerates on a GATED/tiered system. The less energy you have, the less regen you will have (2 to 5 energy/sec). So the best strategy is to maintain high energy levels so that you have high regen levels. When I maintained maximum regen, I was able to keep a group alive without ever going oom.
Unique Mechanic: Tactical advantage works similarly to holy power. Certain abilities (direct heals, hot ticks, some attacks) give you a point of Tactical Advantage. Unlike holy power, abilities that consume tactical advantage only consume ONE point. So you can save it up and use it one-by-one. Most abilities that consume tactical advantage do not use energy, so it's important to rotate TA-generating and TA-consuming abilities so that you regen stays high.
The regular heals are:
1. Kolto Injection: 2.5 cast (2.0 after talents) heal, 25 energy (can generate TA with talents)
2. Kolto Probe: Instant HoT, stackable, 15 energy (can generate TA with talents)
3. Recuperative Nanotech: Instant AoE HoT, 30 energy, has cooldown
4. Diagnostic Scan: 3.0 sec channel, 0 energy
The TA-requiring heals are:
1. Kolto Infusion: 1.5 cast heal, 20 energy, consumes TA
2. Surgical Probe: Instant heal, 0 energy, consumes TA
Other Healer Abilities:
1. Resuscitation Probe: Combat rez
2. Toxin Scan: Instant, Removes debuffs (can be talented to provide direct heal, too)
3. Stim Boost: Regenerates energy in an emergency
In my opinion, operatives and scoundrels can be a lot of fun if you like a dynamic healing rotation. You can only spam your bread-and-butter about 6 times before going oom. Like paladins, operatives are strong single target healers, but they are weak when it comes to raid/party heals. They have no direct AoE heals, and must rely on HoTs to do the job.
Operatives and Scoundrels are close to being competitive. I expect them to be ready at launch. Personally, I would consider them polished if they had at least one direct AoE heal. Ideally, it would be consume tactical advantage. That way, one AoE heal does not need it (the AoE HoT), and the other does (the AoE direct heal).
Mercenary / Commando
Base Class: Bounty Hunter / Trooper
Healing Talent Tree: Bodyguard / Combat Medic
Closest WoW Equivalent: None (lacking abilities) / Shaman (reactive shield like earth shield) / Warlock (!) (mechanic similar to soul shards)
Equipment: Heavy Armor
Primary Stat: Aim
Unique Mechanic: "Combat Support"
Talent Trees: Mercenaries (and Commandos) are, despite the heavy armor, play like a traditional caster. They have two ranged DPS trees, and one healing tree. Mercenary and Commando healing is in need some tuning and extra abilities.
Resource: Mercenaries use heat while Commandos use ammo. While the bars look a little different, and heat is generated in reverse, they function identically to energy. See my explanation under operatives for more information on energy, energy regen, and pacing.
Unique Mechanic: Combat Support is a stackable buff that increases your healing. It is generated by healing others with your free (no heat/ammo) heal, and with your cast heals when talented. Once the stack reaches 30, you can consume your stack of CS to vent heat (restore ammo) and give your abilities a temporary bonus effect (think warlock soul shards) for 10 seconds. Any abilities you use in these 10 seconds can get the bonus.
The regular heals are:
1. Rapid Shots: Instant, 0 heat, generates combat support (3 CS)
2. Rapid Scan: 2.5 cast (2.0 after talents) heal, 25 heat (generates 6 CS with talents)
3. Healing Scan: 1.5 cast, 16 heat, has cooldown
4. Kolto Missile: Instant AoE direct heal, 16 heat, has cooldown
5. Emergency Scan: Instant heal, 0 energy, has cooldown
Combat Support Bonuses:
1. Removes cooldown from healing scan
2. Gives small damage-reducing shield to kolto missile
Other Healer Abilities:
1. Power Surge: Removes cast-time from one ability (i.e. nature's swiftness)
2. Cure: Instant, Removes debuffs (can be talented to provide direct heal, too)
3. Kolto Shell: Shield, 10 charges, heals target when taking damage (i.e. earth shield)
4. Vent Heat: Vents heat in an emergency (same as gaining ammo for trooper)
Mercenaries and Commandos are stable healers, but the lack of Tactical Advantage (compared to operative) makes them slightly more prone to going oom. Also, instead of relying on HoTs to generate your special mechanic (as is the case for operatives and tactical advantage), Mercs do not get any HoTs. Only one ability can be talented to have an occasional bonus HoT attached. Instead, you must top players off yourself using rapid shots, which in turn generates combat support (CS). It feels like more busy work during an instance, for better or worse.
I think mercenaries and commandos need a little more work, but I expect them to be competitive by launch. If they had a HoT that could generate combat support, and perhaps a better way to control heat/ammo, I would consider them polished.
Sith Sorcerer / Jedi Sage
Base Class: Sith Inquisitor / Jedi Consular
Healing Talent Tree: Corruption / Seer
Closest WoW Equivalent: Discipline Priest (absorptive shields), Resto Druid (numerous heal/hot combos), Resto Shaman (similar mechanics to riptide)
Equipment: Light Armor
Primary Stat: Willpower
Unique Mechanic: "Force Bending"
Talent Trees: If you're looking for a very traditional mage experience, Sorceror and Sage are your best bet. Two trees are dedicated to spellcasting damage, and the third is focused on healing. It's very obvious that the most time has been spent polishing this healer compared to the others. It feels the most complete and ready for endgame healing.
Resource: Sorcerers and Sages use force as a resource. It feels a lot like mana, but it is limited. You cannot stack force via gear (it's always capped at 500/600 depending on talents). You CAN, however, improve your regen with gear. The other healers DO NOT have that option, making Sorcerers/Sages unique. A well-geared Sorcerer could theoretically heal forever without ever needing to use regen abilities.
Unique Mechanic: Resurgence is an instant heal + hot (like riptide) that alters the mechanics of your next heal (also like riptide). Resurgence is on a short cooldown (again, like riptide), so you can easily weave it into your rotation. The bonus effect caused by resurgence (called force weaving) only effects the next heal.
The regular heals are:
1. Dark Heal: 1.5 cast heal, 50 force
2. Dark Infusion: 3.0 (2.5 after talents) cast, 55 force
3. Innervate: Instant heal + hot, 40 force, has cooldown
4. Resurgence: Instant heal + hot, 30 force, has cooldown (talented to give bonus on next heal)
5. Revivification: 2.0 cast AoE direct heal (+HoT for people remaining in area), 100 force, has cooldown
Force Weaving (Resurgence) Bonuses:
1. Reduces force cost of Dark Heal by 100%
2. Reduces force cost of Revivification by 60%
3. Increases crit chance of Innervate by 25% (which in turn, when it crits, regenerates force)
4. Lowers cast-time of Dark Infusion by 2 seconds
Other Healer Abilities:
1. Reanimation: Combat rez
2. Purge: Instant, Removes debuffs (can be talented to provide direct heal, too)
3. Static Barrier: Absorption shield (i.e. Power Word: Shield)
4. Extrication: Lowers target's threat and pulls them to you (i.e. life grip)
5. Consumption: Instantly regenerates force at cost of life (like Life Tap), also lowers force regen rate momentarily
As you can see, Sorcerers and Sages have the most toys to play with. They also have the biggest library of heals, and with the force bending mechanic, they have the most versatility and dynamism in their playstyle. Without a doubt, the most effort has been put into polishing these classes, so it's not much of a surprise. I cannot foresee many situations where they would run into trouble.
The biggest hurdle is at the lower levels, you do not have gear that boosts your regen, so you are reliant on pacing yourself. Consumption is best used in emergencies, and not as a regular method to get more force. Sorcerers have no problems with chain pulls, but long boss fights can really put a strain on your force. In comparison, a well-managed Operative can go forever during a boss.