I still like the other poster's 'swimming with or against the current' analogy. It just seems so accurate and sensible, moreso during playoff hockey that is anyways.
The league does seemingly favor certain teams and certain matchups. From the looks of it, if the NHL likes both teams in a playoff series then they'll have a fairly level playing field. If they like one team better than the other, then the ice will be tilted in favor of their preferred team. If 2 canadian teams meet up, it also seems pretty much fair and square. There isn't necessarily any true "fix", but too often there seems to be a slant.
Take 2011 for example. The Canucks built a virtually insurmountable 3-0 series lead against Chicago and the series came down to a game 7 OT. Gillis publicly complained about the discrepancy in powerplays and things straightened out. We were still 1 goal away from losing but it turned what could've been a dull short series into an epic 7 game near-catastrophe.
Another poster mentioned the SCF and how the Canucks got more powerplays in that series. This is a fact, however a great deal of those powerplays came in the games we lost which were all blowouts. We got lots of powerplays when the games were out of reach.
The Canucks didn't do themselves any favors in these two series but the league clearly wasn't on their side either.