It's a good deck but far from broken. It's slow and fair compared to real powerhouse decks like Secret Mage and Raza Priest.
It doesn't help that really aggressive decks can reliably beat you (Big Priest is only a slight favorite). Also there's Counterspell and Oh My Yogg! A good player often only needs to disrupt ONE crucial play against Big Priest to win the game. OTK decks also beat Big Priest.
What decks is Big Priest dominating? Only bad decks.
I put Big Priest at the bottom of tier 2.