I could be wrong but I tend to think that Payton often times closed the gap in the run/pass ratio by running the ball more at the end of games that they had the lead in. That gave the impression of him being "pass happy" because he threw so much early in games. But, I think you can do that when you have Drew Brees and RBs like Pierre Thomas, Bush, and Kamara who are great in the passing game and can be used to sub short passes for runs. Payton clearly liked to set up the run with the pass which meant that sometimes if he didn't get the lead to close out, the run/pass ratio was off.
The Kubiak system clearly sets up the pass with the run.
Anyway, I think either way can work but you have to adjust to how other teams play you and how the Defenses around the league are set up. Payton didn't really do that in Brees' later years or after Brees left. He stuck with setting up the run with the pass which is much harder to do without Drew Brees and with teams playing more 4-2-5 with LBs that can really cover. The correct adjustment is to do what Kubiak is doing, attack those 4-2-5's with an outside zone running game that gets your bigger guys matched up against smaller LBs and DBs. Then once you establish the run, you can play action for big plays in the passing game.