The stakes here cane be summed up in one sentence: Neither team wants to lose their last game of the season to a bitter rival. You should expect plenty of effort in this one, given the history and animosity between these two teams.
The paths to victory for these two teams are what you would expect in a Falcons-Saints game: Avoid turnovers, air it out, and hopefully you have a lead and the ball when there's two minutes to go. Let's get into the specifics below.
The New Orleans defense is almost comically bad, and while you should never bet against them coming through against Atlanta, the Falcons have a pretty easy to path to points on offense. You just run and throw the ball to Julio Jones.
Jones, of course, will be matched up against either talented but gimpy Delvin Breaux or the extremely flammable Brandon Browner, and either way he figures to eat. Getting him the receptions and/or yardage record would be tantamount to lunacy if you're trying to win this game/not grind Julio to a nub, but I think the gameflow will dictate that he gets 15 targets, and he should have a massive game.
Running the ball effectively with Devonta Freeman is not a given—Freeman has been good but not stellar behind worsening blocking for weeks now—but if they can keep the defense honest like they did against Carolina and move the ball at three yards a gallop, the offense will do just fine. Mix in a handful of shots to Roddy White, Justin Hardy, and Jacob Tamme, and this team is in business, so long as Matt Ryan avoids interceptions.
Your only real fear here is that Cameron Jordan will dominate the Falcon's offensive line again, or that the pass rush will generally get home. That's a legitimate concern, one we will have to hope doesn't come to pass.
Defensively, Atlanta can't afford to sell out to stop Tim Hightower—and I can't believe I'm typing that in 2016—because Drew Brees can eat this team alive. They've greatly improved how well they cover tight ends since Benjamin Watson embarrassed them in New Orleans the last time out, but as a team, they'll have to be rock solid in coverage to slow down Brees and perhaps force a turnover or two. Getting a competent pass rush together for the third straight week would at least keep Brees back on his heels, and given that Ra'Shede Hageman and Grady Jarrett have been doing some good work on the interior where Brees loathes having a man in his face, that might actually be possible.
It's worth noting that the Saints' special teams unit is one of the worst in football, too, so don't be stunned if Devin Hester breaks one loose.
You just need to get Tim Hightower and the rest of your backs rolling to the point where Atlanta can't squat on the pass, and let Drew Brees find his favored targets. It goes without saying that Brandin Cooks is shifty enough to mess with this defense and Watson looms as a potential problem, but Brees is good enough to find success throwing all over the field. You've got to make his life difficult, and your options are limited if the Saints' ground game is strong.
Defensively, everything hinges on the team's ability to rush the passer. Matt Ryan has done very well in the pocket the last couple of weeks despite taking plenty of hits, but the Saints present another stiff challenge with some of their talent up front, and with Gino Gradkowski and his unknown performance stepping in at center. Put pressure on Ryan and you'll disrupt his timing with Julio Jones, force some three and outs, and potentially nab an interception or two. That'd probably be enough to win what I fully expect to be a close game.