I have a theory. The Leafs come out looking like they don't want it so often because they hate Carlyle's system. And I can see why, it sucks and is totally inappropriate for the lineup we have. And when the Leafs have an awesome game they do so despite Carlyle, playing short passes and the rush offense. Which is how they want to play.
Interesting thought. Last year they might have still had some habits left over from past coaches. Most of the roster played the first half of the year during the lockout for Eakins, or in Europe. You're not going to change your play style completely overnight, so most guys were probably following Carlyle's system at a high level, but still influenced by how they'd played during the lockout. This year, they've started with a blank slate, and doing everything 100% the Carlyle way doesn't appear to be working. Plus, now he's picked his favorites, they're no longer playing to try and impress the coach.
This is almost exactly what happened to the Pens. The year they won the cup, Therrien was fired mid-season and replaced by Bylsma. During that playoff run, they retained the defensive discipline Therrien had drilled into them over the years, while drawing motivation and better offensive play from Bylsma's contributions. But every year since then they've been horrible defensively in the playoffs and seem to have lost all the discipline they had during that cup run.