I see you've done someone else's homework.
Zone defenses and situationally collapsing aren't particularly visionary or pioneering.
There are also a lot of oversimplifications taking place there - all teams use various systems, which also vary situationally depending on the players on the ice and the context of the game.
"Torts instructs players to overload only in certain situations." That would seem to be a misunderstanding of what overloading actually is. AV also only instructs players to overload in certain situations - when the puck is on one side of the ice, particularly when there is an opportunity to pressure a team when the puck is in arguably the least dangerous part of the ozone, on the half boards. There is no overload unless the puck is to the sides (and relatively contestable), and even in that situation, the weak side forward is charged with taking away the cross ice pass, getting in the passing lane to prevent (risky) passes to the opposing blueline - so "sound positional play" is certainly as much a part of an overload as it is a more passive zone defense and does not distinguish Torts and AV's systems. "Sound positional play" needs to be a staple of any system - how effectively it is executed is another matter.
'Zone' defense is also fairly oversimplified - there are various types of zone defenses.
"Aggressive puck pressure" is more a fixture of overloads and man-to-man than it is with "collapsing", zone, shot blocking intensive defensive formations. If overloading is done effectively, it can reduce opposition possession, and thus reduce the number of shots a defense has to block. "Collapsing" doesn't exactly necessarily imply puck pressure or taking away space, does it? The thing about blocking a great deal of shots is that it does not necessarily indicate effective defensive zone coverage - what it equally indicates is significant possession by the opposition.
Ironically, where Tortorella is perceived to employ more "responsible" defensive systems, his forecheck is an intensive 2-1-2, which is not only more taxing, but arguably more risky, and also puts more pressure on his blueline when that 2 at the front is broken down. When your top forwards are playing some of the heaviest minutes in the NHL, it's debatable how sustainable that system is or how consistently it can be applied.. So whether it has playoff wisdom is one thing, whether your team has anything left in the tank come playoffs, another. During December, it was quite effective, in January, not so much. There are pros and cons to any system, also dependent on the type of players executing them.
AV's 1-2-2 is not as aggressive, and ironically, probably more "conservative" and arguably results in fewer odd-man rushes and breakdowns against the rush.
Both AV and Tortorella like to activate their defensemen significantly and allow them to pinch freely to support the forecheck and to maintain/regain ozone possession.
Imo they're both very good coaches and most statements that reduce either of them tend to be hopelessly oversimplified.
Tortorella's 'systems' have obviously looked horrible recently - but that is as much a result of having a short handed, exhausted team, hammered by injuries and a gruelling schedule as it is Torts' 'systems'. Then again, it just happens that his coaching style is arguably more taxing, and thus might break down a little more quickly when his team isn't all that healthy. It's been stated here that AV never had to deal without Henrik, but Henrik isn't exactly the key to the Canucks' defensive systems, and moreover, AV had more than his share of injuries to cope with at key times as coach of the Canucks.
I find the tendency to proclaim one coach or the other's system's superior to be almost always entirely unsubstantiated, or at best, really reductive.