To me, it depends on a few factors how a 2009 Saints vs. 2011 Saints game would go:
a.) how many turnovers the 2009 defense could generate against the 2011 offense?
b.) how well could 2011 defense stop the run against the 2009 offense?
c.) how much pass rush could the 2011 defense generate vs. the 2009 offensive line?
While they bled some yards, the 2009 defense was 2nd in the league in creating 39 turnovers and an additional 8 in the 3 playoff games. And despite the 2011 offense putting up points like no other, that's exactly how you beat them and exactly how they lost at Candlestick and even to 4-12 Buccaneers team... an opportunistic defense. The 2011 offense turned it over 19 times in the regular season and an additional 7 times in 2 playoff games. While the 2009 offense wasn't very protective of the ball either (turning it over 29 times including the playoffs), the 2011 defense themselves only generated 16 turnovers and 3 additional in 2 playoff games. In 18 games, the 2011 defense generated multiple turnovers in only 4 games where as the 2009 defense in 19 games had multiple turnovers in 14 games. I feel the 2011 defense would likely get maybe one on the 2009 offense, but the 2009 defense would get at least 2 maybe 3 off the 2011 offense in return.
The 2009 offense was far more balanced than the 2011 offense was which led to the 2011 defense more often than not playing with a sizable lead (leading opponents to get pass heavy early). While the 2011 defense was middle of the road regarding rushing yards and rushing TD's surrendered, they were 29th in YPC so teams that could run the ball did so nearly at will, it was just a matter of if opposing defenses would be able to keep them in the game or if they'd get blown out and have to abandon the run (which is why the 2011 defense was 1st in rushing attempts).
While the greatness of the 2011 offensive line isn't in question, the 2011 defensive line is a massive question mark considering no one on the DL that year other than Will Smith had more than 5 sacks. 15.5 of the team's 33 sacks came via blitzing and Harper ended up leading the team with 7.5 that year. While the 2009 offensive line was every bit as good as the 2011 offensive line, the 2009 defensive line rotation proved to be far more potent getting more pressure consistently with only the front 4 and not having to rely as heavily on blitzing (another reason the 2011 defense faltered in San Francisco). The 2009 defense wouldn't have to commit to blitzing as much to get pressure or stopping the run which would free up the back 7 to focus on stopping the 2011 passing attack. The 2011 defense would have to still blitz heavily leaving large passing windows open or risk being picked apart by the 2009 passing attack.
The only thing I really don't know how the 2009 defense would fair with is with Jimmy Graham. We didn't have one of those Aquib Talib or Kam Chancellor enforcer types in 2009 that could just man him up and run with him, however with having
He Who Shall Not Be Named in deep center field could free up Harper having to play 2-high and could just try and bracket him with Fujita or something. However the same could also be said about Shockey since the 2011 defense had largely the same personnel sans Fujita and
that free safety. Don't see Dunbar, Casillas, Herring, or Humber being able to stay with Shockey and he'd still body Greer or any CB on him through sheer size.
In all likelihood, a hypothetical game between the 2009 Saints vs. the 2011 Saints would likely end up in a down-to-the-wire, drag out game like the 2009 NFC Championship was coming down to the last possession. The 2011 offense moving the ball well (and probably at ease sometimes) on the 2009 defense but turning it over quite a bit, and the 2009 offense keeping the 2011 defense on its heels running the ball taking calculated deep shots against the Jenkins/Harper tandem and picking apart everything underneath.