The best I found was at the Beachcorner, the oddly-named bar that's actually located on the corner of one of the cemeteries at the end of Canal Street. The Beachcorner's is really good, in a league with the Port of Call's. What those two have in common is proportion. Very substantial meat patties are made thick, and the bun is the right size for the hamburger. Which is to say, not so large that you can't see the meat.
Some dishes get better as they get bigger.
Steaks, pork chops, oysters, and scallops are that way. But hamburgers are not one of these. Even a big hamburger gets lost on a huge bun. Too much bread, not just in terms of taste and texture, but also too big to get a good comfortable purchase on the thing with your jaws. Or your hands.