Did LSU make the wrong choice picking defense in OT?

By picking offense/defense, it let Bama choose which side of the field they wanted. Bama got to play the OT period away from the entire student section and LSU had to play right next to all of the Bama fans and their band. It felt like they took Tiger Stadium out of the game.

I know it's very conventional wisdom to pick defense first, but is that really the wisest choice always? This is serious. I also think if we went first and kicked a FG, our defense would have played differently to not give up the TD.