Yes, I can seriously claim that they've been more successful than the Capitals AND the Bruins.
To parrot
@Jumptheshark winning the cup is everything. The ultimate goal of every player and every team is to win the cup. More cups = more success.
The cup is the ultimate goal. I'm sure nearly every player would trade 10 President's trophies for a single Stanley Cup victory. There are varying degrees of success which are lower than winning a cup, but the Cup is everything when it comes down to it.
I feel like the President's Trophy gets the right amount of respect. It's nice to have a good regular season, but without a cup it's meaningless.
Edit to add: I do love your Ocelot picture by the way.