When you possess the puck more, you take more shots and allow fewer shots. Offensively, it means more goals. Defensively, it means the other team can't score when you have the puck.
The Habs dump and chase, essentially giving up the puck in the defensive or neutral without pressure for the chance of maybe getting the puck in the offensive zone. What happens though is that you just give up the puck for no reason (either by icing it, losing it in a boards battle or having the puck recovered by a player on the opposing team) and play on your heels.
Teams that carry the puck generally do better than teams that counterattack because they set the tone and set the pace instead of waiting for opponents to make a mistake. To pull off a dump and chase you need to have big, strong forwards who can grind out on the boards.