Why do people think that getting outshot and out-possessed is an actual formula for the Leafs? It's more likely that it's a by-product, not the actual intent of the team. The Leafs struggle to clear their their own end which allows the other team to create some sustained pressure in the Leafs zone. The formula isn't allowing it to happen, the formula is more about what to do when it does happen.
With Wilson's team, there wasn't much structure when the team was forced to defend in their own end. The players cared more about getting the puck or clearing it out out that they opened up dangerous areas for the opposition to shoot through. Not having the calibre of goaltending that we currently do only made it worse because it often resulted in goals.
With Carlyle's team, you see an actual system in place when the team is forced to defend. I think the mentality is that it's better to get stuck in your own end for 2 minutes but try and do all of the little things right than it is to play aggressively and risk the chance that 15 seconds later, the puck is up for grabs at centre ice because the other team just scored on you.