Well we have never lost to LSU except for a tie in 1976 and haven't played LSU since the 1987 Sugar Bowl.
3-1 against Auburn splitting 2 bowl games,our first Orange Bowl win in 1964 Orange bowl and Callahan lost the 2007 Cotton bowl 17-14.
I'd say LSU because they are not very good on offense but is 11th in the country in total defense.
+ LSU is my favorite team in the SEC mainly because of being a huge Maravich fan.But the Outback may take Auburn because of possibly a better record.