Question for the people actually keeping up with the game - If I were to play a Sith or Republic healer which class should I play to be the best? And are the classes on Sith/Republic sides identical to each other?
Sith and Republic ACs are mirrored, yeah. There's only one instance I can think of where an ability on one faction is not mirrored across to the other AC, which is the Sage/Sorcerer level 46 ability. The reason for that is unknown and likely to be incomprehensibly stupid anyway, so it is best to ignore it. Otherwise the classes are meant to be identical on either faction.
As for your healer question, the truth of the matter is it isn't really clear. There are three healer ACs on either faction, and the design intent is that they are all primary healers when they spec into the appropriate skill tree. You'll find that all ACs in this game are pretty much required to heavily invest skill points to move into the healer role capably.
The intent of their parity does not make it
so, but I haven't seen a receipt of any meaningful data to say there's an AC with a significant disadvantage when it comes to healing. I think I'd say from the stuff I have gone over, there's a question of resource mechanics not lending themselves to a level playing field in the long run, but I don't think it's going to manifest itself as a significant issue before BioWare tinkers with things.
Given that we can't make any reasonable assumptions about what they're actually going to mess with regarding healer mechanics and values, your best bet is to stick to their known design goals and go with the AC that has the strongest appeal to you at face value:
The Commando (or Mercenary for the Empire) is a heavy armor healer that is almost exclusively direct-healing based, with the least amount of instant cast heals, but a significant amount of passive buffs and strong utility. Their resource mechanic is ammo; they start at 12 units of ammunition, with each ability using a different amount of ammo per cast. The rate of ammo regeneration is gated; the less ammo you currently have, the slower it will regenerate. This means you must more carefully consider when to rapidly expend ammo, as leaving yourself with little "in the clip" means it will take longer to get that ammo back. There are mechanics in place to further manipulate your stock of ammo, and a big part of playing the class is going to be learning how to best manage those abilities and core regen to maximize your effectiveness. The other two skill trees for this AC outside of healing are for ranged DPS, as the AC is mainly based around the large assault cannon that separates them from the other Trooper AC (Vanguard).
The Scoundrel (or Operative) is a medium armor healer that has the most heal-over-time abilities of all the healers, though they still have some direct healing; they are also the only healer AC also capable of stealth. Their resource mechanic is energy - this works very similarly to the Commando in that it is gated on a curve, so the less energy you have, the slower it regenerates. Like the Commando, they also have additional ways of managing that resource beyond basic regeneration, and the main goal is to juggle those mechanics to get the most out of your energy bar in each situation. They don't have quite as many passive buffs attached to their heals as the Commando, but they are far more mobile as many of their heals are instant cast, so they can handle more healing during movement. They are also (along with the Sage/Sorcerer) capable of resurrecting a player during combat, which the Commando is unable to do. The other two non-healing skill trees for this AC are DPS trees that are mostly melee and short-range focused, playing off their stealth and close-range scattergun off-hand weapon.
The Sage (or Sorcerer) is a light armor healer that has the most varied types of heals of all the healer ACs: cast time direct heals, an instant cast heal-over-time, a channeled single target heal, a cast time AoE direct heal, an instant cast absorption shield, etc. Their resource mechanic is Force, and unlike the other two healer ACs is not gated - the Sage's Force regenerates at a set rate no matter how much of their resource is remaining. They also have the deepest base amount of resource of any of the healers. Compared to the other two healers, they also have the least amount of ways to manage that resource; they have one ability that trades their own health for Force, which once used lowers their current Force regeneration by 25% for 10 seconds (though part of the way the class works after skill points is that they can proc a buff from a particular heal to remove the penalties from that ability). The only other way for the Sage to alter their regeneration currently is through gear via the Presence stat, which is also unique to the Sage. This AC's other two non-healing skill trees are focused on ranged DPS; they wield a lightsaber, but for the most part it isn't something you'll get to hit people with as a Sage.
Pick what sounds like it suits your play style the most. Even if there was a more significant imbalance between them right now, picking your class based on that at launch is probably not the wisest idea, as things likely won't be as volatile in that regard as they are around launch until the game's first expansion.