The Short Version
Sod wins when you need fast results, want St. Augustine or named Zoysia cultivars, have a slope to stabilize, or are selling a house. Seed wins when you have more than an acre of open ground, are planting Common Bermuda or Bahia for pasture or utility cover, and have 8 to 12 weeks to wait through establishment. For most Louisiana homeowners with a quarter-acre yard, sod is worth the extra cost. You skip three months of weeding and babysitting bare soil.
That is the short version. Below is the full breakdown so you can make the call yourself.