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The table pretty much says it all. Firstly, while the West has 12 more non-shootout wins than the East, they're only +11 in terms of goal differential. Generally speaking, a win is worth 5 or 6 goals with respect to net goal differential, so the West should only have about four more wins than the East on merit.
Secondly, the underlying numbers are revealing. The West has done better in terms of the percentages, particularly at even strength, whereas the East has done better virtually everywhere else. Part of the shot differential gap is surely attributable to the fact that Eastern teams have (presumably, given their record) spent more time playing from behind, but it's worth noting the East has still done better with the score close. The East has also been better at generating shots on the powerplay - their six extra PP opportunities can only account for about 15-25% of the shot gap.