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Probably the return flight.
Going First Class and returning Economy always results in an unfavorable comparison on the way back. Also, one perk of First Class is free drinks, which may not apply if you are traveling in the morning.
A factor to check is lounge access before the flight. For example, if the airline has a lounge in LA but not at MSY that could be a decider. If you are on Delta there is a Sky Club in New Orleans, but I don't think any of the other airlines have a lounge at MSY.
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