Like gross overstatements much?
Offensively, you can count the number of Pro Bowls on the Cowboys' roster and the Saints' roster, then compare. You won't see anything approaching vast superiority. And that doesn't even account for Reggie Bush.
It's the coaching job of the Saint's defense that has been impressive.
Payton has not one, but really two defensive coordinators. Gary Gibbs, who was head coach at OU for six years, and "assistant head coach" Joe Vitt, who was interim HC of the Rams in 2005. Both have a ton of experience, both are defensive guys, and in fact both of them are former linebackers who became linebacker coaches. That's their area of expertise, so it should be no surprise that the they were able to get the best out of guys like Fujita and Shanle.
I agree if you're saying Parcells should be more willing to bring in a name assistant, but we're getting carried away with the Payton lovefest IMO.