Here is an interesting fact:
Landry and Johnson both rose in the coaching ranks from the defensive side. However, they have never been ranked #1 in both points and yards for the defense. The Cowboys have been ranked #1 in both categories of offense, yards and points, three times.
The closest the Cowboys ever came to being ranked #1 in defense for both yards and points came in 2003. This was Parcell's first season as a Cowboy HC. They were #1 in yards, #2 in points.
Ironically, the Cowboys ran a 4-3 defense that season only because Parcells didn't have the time or right players to change to a 3-4. They switched the following season.
Getting back to the Cowboys:
The first thing the SB teams all have in common is that they got to the playoffs. This is where we look at their statistical categories. As far as their defensive rankings, they have an equal amount of impressive defenses that didn't get their teams to the Super Bowl despite elite offenses. Look at their conference championship game losses
The difference with Championship seasons was the big defensive plays in the playoffs, especially takeaways. In the 15 playoff games during those 5 championship seasons, the Cowboys amassed a total of 59 takeaways. I think, when we go back and look, that will be the most common thread.