Hey. Thought I would chip in with a bit of my own thoughts on this matter.
End Game as:
Shadow Priest.
Yes, If we look up at WoWWiki Shadow Priests "Melt Faces". I would strongly disagree with this statement since a number of patches back. There damage output is good, but survivability is poor. Unfortunately Shaodow Priests are lacking in CC. They have Black-Out with its %10 Proc Rate, and fear. Though it was once excellent, the fear mechanism is quite screwed at the moment to say the least. Not only does a number of class's have resistance to it through talent spec, there is alse the addition buffs of "Fear Ward". If all else fails they will simply trinket it. Then there is the awkward 22 Seconds (Pr Something like that) or attempting to kite the opponent. And when I say kite, dot and run.
As a Shadow Priest you will also be targeted in PvP. In Arena 2v2 it is most likely that they will direct all DPS to taking you down before you can even kick a heal off. Though going into the Discipline tree for Martydom may be worthwile, it wont keep you alive for long. Shadow Priests have a niche in PvE - Raiding as they are able to Re-Fuel Health & Mana, but in PvP at the moment they are a little ... erm ...squishy.
Holy.
As a Heal-Bot you will pretty much always find a space in Raiding, and most likely Arena. While I was Holy I was partnered with a Warrior and Hunter. We hit the 1900 Rating. Worked out very well. I guess, Its simply what Priests to best. It can get very tedious though, especially while grinding Honour for your S1 gear.
Though with a Holy/Disc build your survivability will be good as long as you have mana. Ive seen 2 Warriors take 5 Minutes to take one down. Was Awesome :)
Discpline.
This tree has pretty much the best survivability. Pain Supression, Reflective Shield etc..the Idea in this tree is to not only be a viable healer, while giving the on-off damage, but to take a pounding and walk away with little but a scratch. It can be fun Spec'ing the tree. Good Buffs and De-Buffs. A very uselful Arena Partner.