Out of interest what is your Priest deck?
Pretty standard, the usual x2 Northshire/Injured Blademaster/CoH/Auchenai soulpriest/Wild Pyro/Power word shield/Thought steal/Circle of Healing/Shadow Word Pain/Death
Rest is 1x Mind Control, 1x Cabal Shadow Priest, 2x Mind vision, 2x Molten Giant, 2x DoA, and two more cards I'm forgetting atm (probably some late game legendary or two).
Weird omissions are holy smite and shadow madness, but I'm not to the point I need to re-evaluate it as I don't play it much outside daily quests.
It often lives and dies by the 6 cards I get from the thoughtsteal/mind vision, but if it makes it to late game, it rarely loses because of the insane value you get out of a well played mind control, and people don't expect the taunted giants in a Priest deck too much, so they don't die as quickly as in a Warlock deck.
I've played a lot of paladins with it, and they usually have a ton of board wipes, but the wipes rarely hit more than a single creature or two most of the time, and at some point they just run out, then it's time for the 8/8 giants they didn't account for, or they finally have to play Tirion in to a Mind Control.
Because it bypasses Battlecries.
Time to start running crazed alchemists if you can get those to stick a turn.