I've honestly never seen labels like "soft" or "smashmouth" as having the final word on a team's quality. We were a finesse team from 2003-2007, but we still won because we executed. That's what it's about to me: execution.
Holmgren's team may not have had a "thuggish" reputation, but he was so fixated on execution and so demanding in practices that the team got it down to a science. Opponents knew exactly what we were going to do, stacked up against it, and it didn't make a lick of difference, because we executed. We didn't lose XL because the Steelers were the better team, we lost because we didn't execute, kept dropping crucial passes (and got rooked by the refs). And our team's decline didn't come because of some "soft" identity that was sitting on the back-burner waiting for its chance to bite us in the ass, it lost because our running attack collapsed from old age/injury/free agency, and got replaced by guys who didn't execute right away.
Similarly, I don't even think we're winning now purely because of our "smashmouth" identity. Our running game is getting a lot of traction because of the tenacity and strength of our O-line, yeah, I'll give y'all that. But on defense, it's not about the big hits or the sacks, it's technique. Our defense has terrific technique, awareness, tackling, and discipline all across the board. You can hit people hard all day, but if you blow an assignment the next play or allow leverage to a WR, there's no point. Our defense executes.
Same thing in Dallas. I suppose I can't disprove the idea that we had an undefinable psychological edge in that game, but we didn't win just because of that. We won because we executed better than Dallas, cut down on our penalties and made timely plays while Jason Witten and Dez Bryant kept dropping passes.