The total stats show how LSU was "overall" able to move the ball better than Bama, but what they don't show is how the teams played once they got into opponents territory. I like to break down the games by looking at what the teams do after they cross midfield. Here is what I came up with a quick tally:

LSU:
Crossed midfield an impressive 8 times plus got the punt fumble
scored 3 of 9 times (33%) - 2 Td's and FG
missed 2 FG's, missed 2 4th down attempts (1 was fake FG), 2 punts
7 First Downs
27 rushes for 61 yards (2.3 ypc)
completed 9 of 16 passes (56%) for 65 yards (7.2 ypc)
4 of 9 3rd down conversions (44%), 0 of 2 4th down conversions
126 total yards

Bama:
Crossed midfield 5 times
scored 3 of 5 times (60%) - 3 Td's
punted once (after offensive pass interference call) and a fumble
7 First Downs
11 rushes for 72 yards (6.5 ypc)
completed 7 of 9 passes (78%) for 80 yards (11.4 ypc)
1 of 2 3rd down conversions (50%)
152 total yards

As bad as it looked at times, these stats show that "when it mattered", Bama played better football (even AJ).