This post is SOLELY debating their respective offenses, not overall teams.
The 1999 Rams went 13-3, scored 526 points, had 66 TDs (42 passing, 13 rushing, and 11 defensive or special teams), had 6412 yards of total offense (4353 passing and 2059 rushing), and scored 40+ points in four games (3 in the regular season, 1 in the playoffs).
The 2011 Saints went 13-3, scored 547 points, had 66 TDs (46 passing, 16 rushing, and 4 defensive or special teams), had a still-standing NFL record 7474 yards of total offense (5347 passing and 2127 rushing), and scored 40+ points in seven games (6 in the regular season, 1 in the playoffs).
Regarding turnovers:
The Rams had 31 total turnovers resulting from 15 INTs and 16 lost fumbles out of 30 total fumbles.
The Saints had 19 total turnovers resulting from 14 INTs and 5 lost fumbles out of 9 total fumbles.
Regarding both teams' opening playoff games:
The Rams scored 49 in their opener (divisional round at home) against the 10-6 Vikings who were 2nd place in the NFC Central and 18th in scoring defense. Their offense accounted for 42 and their special teams got 7 on a kickoff return.
The Saints scored 45 in their opener (wildcard round at home) against the 10-6 Lions who were 2nd place in the NFC North and 23rd in scoring defense. Their offense accounted for all 45 points.
Regarding both teams' second playoff games:
The Rams scored 11 (9 on offense, 2 via safety) in the NFC Championship game at home against the 11-5 Buccaneers who were 1st in the NFC Central and 3rd in the league in scoring defense.
The Saints scored 32 (all on offense) in the divisional round on the road against the 13-3 49ers who were 1st in the NFC West and 2nd in the league in scoring defense.
The Rams would go on to score 23 in the Super Bowl (offense accounting for all 23 points) bringing their postseason tally to 83 points of which their offense was responsible for 74.
The Saints' offense accounted for 77 points in just two games against roughly the same caliber of defenses. The Rams' three playoff opponents' scoring defenses' rankings averaged out to 12th and they averaged allowing 298 points. The Saints' two playoff opponents' scoring defenses' rankings averaged out to 12.5 and they averaged allowing 308 points.
"But the Rams at least won the Super Bowl!"
True, but they played in an NFC where the best team outside of them was 11-5. The Saints played in an NFC with the 15-1 Packers and the 13-3 49ers and ended up playing wildcard weekend. The Rams were also getting considerably more help from their defense.
The Rams were able to win a conference championship game scoring only 11 points. The only teams the Saints would've beaten with 11 points in 2011 were the 5-11 Jaguars and the tanking for Andrew Luck Colts.
The odd thing is that I didn't initially go into this stat hunt eagerly curious to see what kind of crazy stuff the Rams had done. I'd gone into a massive rabbit hole of first trying to see if my assumption that the Saints had never beaten the 49ers in a meaningful game was correct. While researching that, I began paying attention to the ultra-rare instances of the Saints either scoring 40+ points in a game or racking up 500+ yards prior to the Payton/Brees era and then noticed the predictably sharp spike after their arrival.
After seeing that the Saints had notched five separate 500+ yard games in the 2011 regular season, I wondered if the Rams had done so even more times. Then I found out they hadn't even done it once. That led me to become even more curious and motivated to find out what exactly it was that was keeping the Rams right up there with the 2007 Patriots and 2013 Broncos on almost every hack internet journalist's "aLl TIm3 gR8e$t awfencez" lists.
Maybe people just look at Marshall Faulk's 2429 yards from scrimmage and decide that that's all that matters. I wonder if those same people look at Drew Brees' 1123 yard advantage over Kurt Warner's passing yardage total.
Anyhoo, if any of my fellow sports nerds can think of any points that empirical data supports, I'm all ears.