From favorite to least favorite:
EAT's version won on the basis of being an excellent melding of flavors without a musty taste. Since the liquid wasn't quite a thick as versions that my husband and I didn't enjoy quite as much, I suspect EAT's version had little/no file powder. I know file is an essential element in thickening and flavoring an authentic gumbo, so I guess I'm not a fan of authentic gumbo.
We made our lunch choices on the basis of being the best conveniently located restaurant, but we didn't do destination lunch eating. If there is a destination gumbo place, I'd sure like to hear about it.
Incidentally, the lunch at EAT (900 Dumaine) turned out to be one of the food highlights of our trip. We went to this restaurant since it was both close and recommended by our hotel. For our first meal in NO, we ordered generously: Gumbo, fried green tomatoes, fried chicken livers, and bread pudding. The kitchen's frying skills were very much in evidence on the two fried dishes. Both were served with the best Remoulade sauce I've ever eaten. The menu claimed the livers would be served with pepper jelly, but came to the table with Remoulade sauce. One bite and we didn't care about the missing pepper jelly. (One small criticism: Two of the tomato slices in the plate of fried green tomatoes were cut too thin and the coating-vegetable balance was off.) We were stuffed from our meal but we heard our waiter praising the bread pudding to the diners at the next table so we ordered a portion. This was the lightest souffle bread pudding we've ever eaten. Furthermore, the whiskey sauce provided just the right bite to the finished product. Definitely not too sweet. We were never in the neighborhood again at lunch time or we would have happily eaten another meal there.