I've heard so many good things about all 3 and realize they are all very different, but I honestly can't decide! Please Help!!! Our other meals are: Mr. B's for lunch, Brigtsen's for dinner, Camellia Grill for breakfast/lunch.
I would pick Dick and Jenny's simply as it is my preference over the other two. I have heard both wonderful and not so wonderful things about Gautreaus, and as I have not been there in a Looooooong time I cannot say. I like Cochon, but prefer lunch and not dinner.
We have dined at Gautreau's four times over the last couple of years. Wonderful place, but, for the money, you can have a better meal at numerous other "fine" dining places. Not bad meals, just b or b- for new Orleans. We keep trying to like it, but have given up.
We just got back and loved Cochon, although we haven't done the other two. We found a great local neighborhood breakfast place too - Commerce Restaurant on Camp St. just a block from Canal St. and Magazine (if you're staying in that area).