My conclusion was implicitly premised on the assumption that there's no significant skill difference between the two conferences with respect to shooting or save percentage. The rationale behind that assumption was that, while there are talent differences between teams in terms of the percentages, those differences should cancel out when comparing large groups of teams. Without taking a further look at the data, however, it's impossible to determine whether or not the assumption relied on is true.
In determining the above issue, I think that it might be helpful to look at data from interconference games over the last six seasons. I'd delve back further in time, but 2003-04 is the oldest season for which I have advanced statistics at the team level. It's well established that the West dominated the East over this timeframe, as evidenced by the table below. The West had the better record in each of the six seasons examined, with an aggregate winning percentage of 0.54. That's only slightly better than what one would expect on the basis of their goal ratio (its expected winning percentage was 0.536).
[The % column indicates the number of percentage of East wins/goals/shots/powerplay opportunities as a percentage of overall wins/goals/shots/powerplay opportunities. For the post-lockout seasons, games that went to a shootout are considered ties. Empty nets goals have been removed from the data.]
In order to determine the nature of the West's dominance, however, it becomes necessary to take a more granular look at the data. This can be achieved through looking at how each conference has done in terms of shots and the percentages, through breaking down the data by game situation (even strength and special teams), and through looking at data from when the score was tied in order to identify and/or control for playing to the score effects.
[I elected not to include data on shorthanded shots and goals given that shorthanded scoring is neither an important nor sustainable component of team success].
The first thing one might notice is that the West did better than the East across the board - both at even strength and on special teams, and both in terms of shots and the percentages. It was also a fair bit better on drawing penalties, which is noteworthy given that NHL referees tend to favor the trailing team -- Eastern teams presumably would have spent more time playing from behind than Western teams during the games sampled.
However, while the West has technically outperformed the East in respect of shooting percentage, the difference is marginal. Indeed, there's effectively no difference at all at even strength, and while the difference in terms of PP SH% is larger, it's not necessarily reflective of an underlying talent advantage. For example, if the two conferences had the same "true" PP SH%, one would expect one conference to have an advantage of at least 0.004 approximately 50% of the time.
Similarly, the fact that one conference tended to outperform the other in terms of EV SH% in specific seasons should not be construed as meaningful. Random variation requires an average difference of 0.00468 when comparing the shooting percentage of one conference to the other. The actual value? 0.00467.
The success of the Western teams was driven primarily by its outshooting advantage, and this was true at both even strength and on the powerplay. The fact that the data for this season shows no such advantage for Western teams suggests to me that it may no longer be the better conference. While it's true that the West has done better than the East in relation to the percentages, it's difficult to interpret that as a difference in underlying skill for the reasons outlined above.