First of all I made the post where I believe Gudbranson shouldn't be paid over 4 million, and should be paid less than Tanev who is a superior defender.
But that's not to say intimidation and physical play doesn't have value.
Couple examples:
1. If two dmen are as good at limiting shots at the net. Does it matter the means/style?
For example if Olli Juolevi plays 1 shift against the other teams top line and generates 0 shots for, and 3 shots against.
Gudbranson does the exact same, 0 shots for and 3 shots against.
Are they equal defensively?
What if Olli did it by staying in passing lanes, and using an active stick. While Gudbranson was able to lay a couple more hits and some crosschecks (unpenalized) to the opposition?
Is there not more wear and tear on the opposition? Wouldn't the "style" that Gudbranson plays increase the chance the other team can suffer injuries?
Wouldn't that be advantageous in a 7 game series? Weren't injuries one of the reasons the canucks lost in the finals?
2. Hockey is about momentum. Are there any advanced stats that track momentum shifts in a game, and who was able to create a momentum shift?
It could be a timely timeout, a timely goal, a timely save, a big hit, a fight that lifts the bench etc..
That physical element can be a source of potential momentum shift. But the momentum shift might not be accounted for in "that" player's advanced stats. A positive momentum shift can be a boost to the entire team.