Green Bay and Atlanta have better receivers, New England has better running backs and playcalling, and the Peyton Mannings are more efficient. I wouldn't crown the Saints the best offense in the league at all.
New Orleans allowed "only" 28.4 ppg this season, a massive outlier considering how far they led the league in yards allowed. They lost their 8 games by the following amount of points: 8, 8, 3, 1, 20, 10, 10, 25, 6. Even allowing a TD less a game (21.4 ppg allowed would have been 12th in the league) would have only gotten them to an 11-5 record!
It doesn't really matter who between the Falcons and Saints are better, because they're likely to split their games next season and every season because they're so close. Who makes the playoffs is really going to come down to how they do in their out of division games, namely the NFC East opponent (Saints are vs Cowboys, Falcons are vs Redskins), the Patriots (Falcons at home, Saints away), the NFC North opponent (Falcons @ Packers, Saints @ Bears), and the NFC West opponents (Saints vs 49ers and @ Seahawks, Falcons @ 49ers and vs Seahawks). Both teams are going to have trouble having a winning record against those five teams.