A lot of people (in various forums) seem to be debating which healer is going to be best, so to break it down a bit based off their skills and skill trees I feel its safe to say:
Once you choose an Advance Class (AC), it cant be undone, but you CAN respec your skill trees for any one AC. keep this in mind when choosing. All of the healer classes have different resource systems, but each of them has at least one small, spammable, "free" heal that doesn't use any resources. It won't be enough to get through tight spots, but it will make resource management tolerable.
SI sorcs will have castable damage shields (think wow priest PW shield) and channeled or cast timed heals (mostly reactionary) with a recharging, mana-esque resource. It has a battle res. Its dps respec is a typical caster: cast timed burst spells, as well as some channeled DoTs and large aoes.
IA opers will have a single target HoT heal and then cast timed and reactionary instant heals with a constantly recharging energy system (think wow rogues). It has the ability to stealth and it has a battle res as well. Its dps respec is a melee class that can specialize in burst damage or poisons. It has some ranged skills, but not enough to keep it out of melee range effectively.
BH mercs will have a reactionary healing shield castable with multiple charges on a single target (think shammy earth shield from wow). and then the typical healing skill set. It uses a heat system that builds up with skills and dissipates over time, with a few mechanics to help lower it back down and a number of heat-less skills to keep it low. It does NOT have a battle res. Its dps spec is a ranged class that has some CCs and can either burn through all its heat in a quick burst or use a more sustained rotation to keep heat low (pvp vs pve maybe?)
It appears you can pick and choose from the specialization trees, but i doubt you will see such a mix too much in pve, but will likely be prevalent in pvp for a mix of survivability and dps.
I know some people only care about numbers, but for those who care about how a class plays, I hope this helped.
The Mercenary has 3 skill trees that you can spec into. Here's a little description of them (leaning towards pvp)
Bodyguard - Healing tree, don't know that much about it, supposedly decent but not quite on par with inquisitor/consular healers atm.
Arsenal - High DPS "caster" class. Has very high burst damage and good AoE damage, but is lacking in mobility and cc. If you want to play Arsenal well, then you need to be standing still casting (Tracer Missile) whenever you have the chance, basically a static turret. Has some problems dealing with melee classes and contrary to what a few people think, it is not a good kiting class, as you don't have enough stuns snares or movement impairing effects, and you need to channel a lot, so people can just move out of LoS or interrupt you. But overall extremely good damage and one of the best DPS specs right now.
Pyrotech - This is a DoT tree that is more mobile than Arsenal but has much less burst damage. You want your target to be burning at all times (Incendiary Missile) as this does decent damage over time and increases the damage of a lot of your abilities. It is more of an instant ability class rather than casting like Arsenal, however some abilities will still need channelling such as Power Shot and Unload, but overall it does have more mobility and you can fire off your attacks on the run. The general consensus is that this tree is inferior to Arsenal, however it is more balanced in terms of blaster to missile usage, so if you dislike the missile spam of Arsenal and want to use your duel blasters more, whilst lighting stuff up, then Pyrotech is an option for you.