I don't know where you saw this apparent consensus that he was a "traditional union-busting Republican" (which I assume would be along the lines of Walker/Kasich/etc), but I don't think it was here. In my opinion, Christie is more or less a moderate Republican in the same way that Huntsman is seen as one. Fiscally conservative (but not extreme), realistic foreign policy views, socially moderate (civil unions, environment, drug war, etc), and has a desire to work with Democrats in order to help his state over helping his party.
Christie is always going knuckle-to-knuckle with the state teachers' unions, specifically. But what else is new? Every GOP New Jersey governor seems to run afoul of the NJEA at some point.