As an active member of the 85 pvp scene, I prefer playing disc, you are pretty hard to cc with sw:d, ward, scream awesome heals. The only hard counter you have are good death knights in which if you don't get peels rather frequently, you will without a doubt, be facerolled into the ground.
I'll make a quick list on what I see for all classes (with their pvp spec obviously)
warriors- Arms. They do great damage, but are pretty easily cc'd and the chances of them killing a good healer excluding priests if you have a high skill cap, are very slim.
Warlocks- ATM, an insane class with enough cc to 1v2 low mmr games. They are not very squishy with your pet up, and are extremely hard to land a kill on with maps like valor, blades edge. (tele up top and /lol @ opponents slowly running up as you soul harvest in their face.
Druids- Now 2/3 of their specs are pretty viable atm. Boomy is really great for spellcleaves, pop cds and shit just dies. They are most viable with spicy chicken atm, (Fmage,Boomy,disc). Ferals are by far the most annoying fuckers in arenas imo from a disc perspective. They have insta clones constantly proccing, and if you play it right, you won't have the natures swiftness or w.e it is called insta dispelled.
Mages- Frost/Fire are the specs of choice. But if you are insanely good (r1 glad status), you can pull off arcane because if you can get arcane blast stacks going off, you will out damage frost and fire by miles, except you have hardly any survivability. Frost is the more common spec mages play due to its kiting ability and stupid shatters on people in a smoke bomb. Fire is good for games when you don't typically go for a kill in the opener. You have DB, which is a great 4 second disorient with a low cd. A good cc healer- spread combust and make sure it won't get dispelled is insane damage and commonly lands you a kill. Cauterize is also a great spell unless you are playing a good disc who will realize you are going to instantly block when it procs (insta mass dispel).
Death knights- These guys are the bane of all healers if they are good. Unholy is the spec of choice for high rated players( sometimes you can get away with frost if you are playing a comp i.e rogue,Fdk,Healer were burst is a bigger factor. But they are very hard to cc (especially as a disc). Fear into lich/trink. A good one will insta dispel lich so they can't be chained. Grip inner focus heals. Stack a billion necros-etc.
Rogues- These guys are probably the best arena class at the moment. You will see most high teams are rls/rmp. They have bomb-TONS of cc/op recup survivability/ and great burst. They are an all around solid class, with an extremely high skill-cap. Don't play a rogue unless you know exactly what to do at all times. Missing a focus kick-resap, etc is game changing and can get you a loss if you can't pull it off almost flawlessly.
Priests- Disc/Shadow are the viable pvp specs. Disc is great survivability except as stated before if you are fighting a good dk. They can oom healers- have a double dispel, great assist burst with a properly timed fiend, and spike spamming. Shadow is also a great spec, best to roll with a good shadowplay and again, shit just dies. A problem you may run into is, you are easily trained, and with disperse down, very squishy.
Paladins- Holy/Ret- Ret is typically not a huge burst class when playing a team that will instantly dispel your wings. When wings are down you do pretty sub-par damage, but have insane self heals and wog to be honest is pretty overpowered. Holy is a solid healing class- they are easy to cc though.
Shamans- Now every shaman spec is viable if played by the right person. Enh is great damage with their wolves. Ele is pretty squishy not going to lie, but they do insane damage when giving the opportunity to free-cast which is typically rare. Resto is just straight up op currently. They are the best healers in the bracket right now, and every 30 seconds can throw out a hex that a lot of the time can not be dispelled. Their heals are amazing along with earth shield, unless you are a dk, don't plan on being able to kill one as a dps.
Hunter- Last but not least, these guys do great burst and have great cc but little survivability. A proper scatter-trap is game changing. They are played really commonly in jungle cleaves and *sigh* scummy triple dps.
Hope this helps you out if you decide to read this wall of text. T.L.D.R?