I was 3-boxing before using Paladin, SPriest, and Holy Shock Pally and I did not like the SPriest.

The SPriest took much more micro-management to drop the cast sequence and dps rotation.
Later, I switch to a Smite Priest build and it was ok--but still felt slow dps--and longer down time as I needed to drink up to get mana after pulls.

I was doing Shadow Labs first room at the time too.