It's roughly 80 miles from Baton Rouge to New Orleans. If you car gets 20 MPG, that's 8 gallons of gas. @ $2.50/gallon, that's $20 a day to drive. How is the train any worse?
If you ride the commuter trains up here, New Haven, CT, to Grand Central Terminal, NYC, it's $11.50 during off-peak times, and $14.00 during peak times, one way.