Week 13 Post-game AMA: Back to the drawing board
For what it is worth, four of the top five scoring defenses this season run a 3-4.
This really has to do with pressure more than anything. Gameplanning against an odd front is always way more difficult than your standard, 4-down over or under front. Keeping track of where that 4th rusher is coming from, as well as pressure (5+)... it's why most teams, regardless of base defense, move to reduction front on passing downs.
In truth the Saints--while they do maintain a mostly 1-gap, over/under structure--usually have one or both edge rushers without their hand in the ground. The way a 3-4 vs 4-3 front is defined is really way more blurred than it used to be. Now it's more about personnel and how you fit gaps. Who's 2-gapping and where? Are you using more head up/tightly shaded techniques on the DL (a 4 or 4i with the ends)? And how, where, and with whom are you pressuring?
Just like offenses, defenses have become way more multiple in recent years. My general philosophy is go bring in the best players you can at specific units and tool your scheme to your talent. Yes--you have your philosophy and maybe your overall structure set, but be multiple and be schematically intelligent about what you're going to major and minor in.