Pretty much every sentiment in this thread has a degree of truth. Paladins, with their heavy armor and the infamous bubble, are rock-solid healers that make opposing teams groan. Priests have more vulnerabilities, particularly to rogues, but have superior offensive potential.
Offensive dispeling is quite powerful, especially as it can nab both offensive and defensive spells. Blessings, damage shields, buffs, HoTs, all of it is fodder for dispels. Do you know how stupid a three-minute mage looks when you dispel his AP? On rare occassions (against people who don't use macros well) you can even get PoM and Nature's Swiftness, and that just drives people nuts.
Additionally, priests have Mana Burn. If allowed to cast this unmolested, Mana Burn is unbelievably damaging to an arena team.
All of that said, priests are squishy. Really squishy. We rely very heavily on our instant-casts to survive, and if those aren't enough, a whole world of abuse can be turned on us. We have no inherent class protection against snares and (particularly) poisons. And few classes die faster to focused fire. Priests are PvP tanks, and have similar gear requirements (heavy stacking of stamina and resilience).
Paladins will always have the bubble (unless a clever priest mass-dispels or it he lets it get locked out), which can get them out of some really bad jams. They have an additional anti-physical bubble that can drive some teams nuts. The huge armor differential alone is a big plus, in addition to built-in protection against snares (Blessing of Freedom) and poisons (Cleanse). Their offensive potential is quite limited, however, and they have no inherent mana regeneration abilities. When a paladin's mana is gone, it's _gone_.
I enjoy my priest in arenas. If you enjoy your priest, I think it would be senseless to re-roll just for arena. Arena-ing as a healbot priest is a hard path to follow, but it's quite rewarding.