The difference here I think is that Payton would be far more valuable to the Cowboys than Arians was to the Bucs at the time. I think the Saints have enough leverage to get some substantial compensation.
He's definitely more valuable, the problem is that the leverage will be diminished once the Saints have a new coach in place.
Say in a year Payton says, "Okay, I'm refreshed and ready to coach again." The Saints will have his rights, but with another coach under contract (and potentially a whole new staff) it seems their options would be to either (1) say to Payton "you have to come back to us" and dump the new coach (and pay off the rest of his contract) to force Payton to return against his wishes or (2) to honor Payton's contract to retain the rights to him but effectively pay him $15 million a year not to coach.
Either way you're looking at paying a lot of money, all in the interest of throwing up a roadblock against the greatest coach in team history to prevent him from moving on with his life and pursuing future opportunities. I just don't see that happening.
TBF the Cards ownership are the same people that have unjustly claimed the 1925 NFL championship over the Pottsville Maroons despite the latter's victory over the Cards in what was billed as the "championship game." I worry that Gayle Benson and Mickey Loomis might not have the same desire to wring every advantage out of the situation that the Bidwills do.