The Western Conference has had the better record in interconference games in each of the last ten seasons. That trend has continued into the current season, with the West putting together an impressive 67-50-20 against their Eastern counterparts thus far (games that ended in a shootout are counted as ties). However, upon closer inspection, it would appear that the two conferences are much closer to one another in relation to ability than the results of the interconference games would suggest.
[Note: The data in the table was calculated after removing empty net goals]
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.