It's a good question, but typically teams have an identity. The Devils during their great years certainly had one. Which is not to say they couldn't generate offense, but they were a tough defensive team. That was who they were.
Edmonton in their hey day. The broadstreet bullies, the Isles with Trotz have adapted an identity, etc. I think Boston is a team who has stuck to an identity for ever.
Now like I said above you do want adaptability, when your down a goal in the 3rd a good defensive team needs to open things, and the converse is true of a good offensive team with a lead in the 3rd, but when you show up to the rink for a game, I think you want to know who you are.