Florida/LSU on neutral grounds?

I would love to see Florida and LSU play each other on a neutral field each year, kind of like the FL-GA game. Each year, Florida/LSU is one of the biggest matchups, if not the biggest matchup for each team on their schedules. I'm not saying just because the game is being played in Baton Rouge... which means the Gators will lose... LSU would be favored to win regardless of where the game was played. If the game was being played in Gainesville, LSU would be favored to win there too, by the media and by me. I just think in the most recent couple of years, the winner of the game has changed depending on where it is played. While the two schools aren't really "rivals", it is arguably the biggest game of the year for either team, each year. What are your thoughts? Also, if they did play on a neutral field, where would you like to see them play?