Only recently did Camyron respec back to PvE healing. If you want to look him up in Armory, you'll see that he's done his fair share of arenas.
For the most part, his arena team consisted of two warlocks (one demonology, and one who constantly respecced between demonology and a draintank build) and himself. Inevitably, as the primary healer for an arena team, you end up also being the primary tank.
For the most part, I took a strong liking to this
PvP Holy Spec. It gives you access to improved mana burn - which is vital for any pvp priest spec, all three passive defensive talents (Martyrdom, Blessed Recovery, and Blessed Resilience), and believe it or not, Circle of Healing. As a holy pvp spec, I have less pure damage mitigation than other specs, but the ability to spam a manacheap, effective, and (most importantly) instant cast (ie unspell-lockable) heal was paramount. It wouldn't keep me up forever, but it gave my two warlock buddies more than enough time in most cases to clear the match. Lastly, let's face it: Spirit of Redemption rocks in the arena, especially if you happen to have a
Twisting Nether Card. Just a thought.
At the end of my arena-ing (as it were) I switched to a
PvP Discipline spec. This spec is based more on damage mitigation, but you'll have to be more careful with your mana use. With this spec you'll take Greater Heal right off your bar and rely almost solely on PoM, Flash Heal, Binding Heal, and renews. The nice thing about this spec is Power Infusion (generally on a dps caster ally) and damaging shields. I didn't play this spec as long, but I did find that my survivability had greatly, greatly improved.
For the most part, which spec you choose will depend on three things: Your gear, your playstyle, and your opponents. The last you cannot decide, so - like most things - it'll end up being situational.
As far as priests are concerned, they excel in arena in two categories: Buff/Debuff control with dispel magic (dispelling elemental mastery off a shaman or arcane power off a mage can be gamebreaking moves), and AoE healing, especially with Prayer of Mending. As a group with two warlocks, we actually found enemy priests to be a challenge much of the time when, after DoTing up our three opponents we hear the incessant "ding"ing of a Prayer of Mending going haywire.
However, in my experience, priests at this time are not the "premier healers" Blizzard told us we'd be. So here's a brief breakdown of the healing situation as it applies to all:
Priests:
Strong heals w/long casting times and poor mana efficiency
Unrivaled AoE healers: Prayer of Mending, Circle of Healing
Less spell-lockable with a small assortment of instant-casts
AoE Fear is their primary defense: Say hello to the fact that half the classes in the game have ways of breaking it.
Shadowfiend *can* be killed, but is generally reliable mana recovery
If the priest has time, mana burn will win the match
If the priest has time, dispel magic can be immensely powerful
A priest almost never has time...
PW:Shield is overrated - it is not a defense, it's a timebuyer
Paladins:
Strong heals w/shorter casting time and outrageous mana efficiency
More spelllockable than other healers
Divine Shield can be prevented by spelllocking
Divine Shield can be dispelled by a priest (if they have time)
No instant cast healing is a liability
Very mana-drainable, but...
A paladin will never run out of mana. Never. It doesn't happen. I know. It doesn't make sense. Mana burn, whatever. They never stop healing. You have to kill them.
Fortunately, once they've bubbled, they can be nuked and spell-locked. They can't heal through damage like other healers, but this will still be very dps-dependant.
Druids:
A 2v2 nightmare with warriors - this team is unstoppable
Can stealth until healing is needed
Strong instant-cast HoTs allow druids to LoS, run, and evade
Nature's Swiftness is Lay-on-Hands without the mana cost
Very mana efficient, + innervate
Cyclone is useful but overrated... as a healer I found getting cycloned more comforting than alarming. 6 seconds of immunity. I can more than make up for the lost time in exchange.
Shamans:
Mana inefficient, but powerful healers
Totems can serve versatile purposes
With the right gear, a shaman can lesser healing wave spam through the most brutal dps - it's actually fairly silly.
Very short heals, but shamans are still very spell-lockable
Nature's Swiftness is Lay-on-Hands without the mana cost
Defense measures that require totems can be unreliable
Despite a lot of drawbacks, shamans are still formidable healers
While I'm definately more an authority on priest healing, I'd be glad to offer my advice on any more specific questions you'd have. In my experience, the most feared healers are paladins and druids, especially when on a team with a warrior. In my case, paladin's bubbles kill all DoTs and as the primary healer I oftentimes had no opportunity to dispel it. In the case with druids, we simply couldn't keep them properly targeted the majority of the time. I could dispel their spells, but it's more costly for me to dispel than for the druid to simply slap more HoTs on. Personally, I would suggest going with a Resto Druid for endgame pvp. They inevitably top healing charts on BGs without even thinking about it, and their sheer ability in arenas to stay away and out of LoS of enemies makes them an incredibly powerful healer in and of itself.
Hope this was less of a rant and more of a help. If you have any other questions or comments, feel free to ask and I'll do my best with what experience I've got.