Interesting question. I guess starting off with my definition. I see grit as being a mix of toughness (hits, getting to the hard areas, mental fortitude) and getting under the skin of a team (sticks active around teams ankles, hits are more borderline, love to participate in scrums)
For me I see the Wild, Bruins, and Kings (in that order).
I am having a hard time picking a softest, I don't see a 2010-11 Vancouver team amongst this playoff group; which is my guideline for soft (or maybe they were just against an insanely gritty bruins team).
Out of the teams I have watched (so not Rangers, Panthers, Hurricanes, Islanders) I think maybe Avalanche. Simply because their game is so fast and skilled.