The New York Giants proved last season that having the best defense in the regular season isn't necessary for winning a Super Bowl.
However, a good - if not great - defense sure helps when a team is working its way through the NFL postseason tournament. Several of the teams in this year's postseason give up plenty of yards, but then survive by getting teams to turn the ball over. Several of the teams specialize in getting after the quarterback, while others are good against the run.
However a defense does it, getting the ball back to the offense is always going to increase a team's chances of winning in the playoffs.