Priest battles come down to two spells: Mana Burn and Silence.

Open your battle with 2 dispel magics, and then start casting Mana Burn. You should catch him doing the same if they know what they are doing.  If you get your burn off first, then (if he is still casting) silence him.  If his goes off right before yours, pop a renew on yourself, then a Rank 1 SW:P on him and silence him. Most priests will see the DOT and not realize that it is a Rank 1, so they will spend their first precious moments out of Silence dispelling your cheap spell. That being said, if you receive a DOT, dispel it after checking to ensure he is not pulling the same trick on you. If you get a chance, close on the priest and fear him, but concentrate on Mana Burn, and random dispel magics (pull off his renew’s, etc). When the other priest (hopefully not you) runs out of mana, start laying into them with Blast/Flay/Smite until they are dead.  Do not be afraid to close and smack him with your stick either

If the other priest is shadow, do NOT cast Shadow Protection on yourself – the spell is expensive and a good priest will recognize the animation and dispel it.
 

A priest fighting a priest can expect for one priest to win 100% of the time.