So, since 2006...
Only the Pens, Bruins, and Canes have won the cup in the East. I would say that the West has a pretty tight grip on the reigns at this moment. What is worse is that the Western Conference teams have to be deep enough to make it through their wars of attrition just to get to the cup.
Even worse is that there are teams in the West who with just a piece or two could be contenders, this isn't going to get better until a good coach and GM figure out how to play a Western style and still win in the East.