Hi Ruddy... nope, I've never taken the train anywhere! However, I checked the addresses of the Amtrak and the Port... when I google mapped it, the results said it's between 7 and 9 minutes between the two depending on which route is taken and the traffic.. and less than 3 miles.
The information i received from the NO travel guide said this about taxis: "Rates are $3.50 plus $2 per mile (or $0.25 per 1/8 mile) thereafter. During peak visitor times or special events, taxi rates may increase but will be posted. A fixed rate of $33 (two ppl) is charged from the airport to most areas in New Orleans; for parties of more than two, the fare is $14 per person."