Bronx, definitely -- Golden-headed Quetzal, Lesser Bird of Paradise, Lesser Vasa Parrot, Splendid Sunbird, White-crested Hornbill an entire colony of White-throated Bee-eaters -- very cool place. The Aquatic Bird House is also nice but World of Birds excels in comparison.
Denver's was very nice and had lots of rarities back in 2002 such as Toucan Barbet and Blue-naped Chlorophonia.
I remember San Antonio's being very dark but having a fantastic collection in 1997. Almost every exhibit had 5 or more species, some upwards of 15.
Philadelphia's is new and while it only has four major sections, it's clean, the birds are very tame, and the overall impact is great. Notable species -- Crimson-rumped Toucanet, Ivory-billed Aracari, Little Tinamou, Yellow-knobbed Curassow, Hawaii Amakihi.
National Zoo's is OK but always seems empty to me. Some great rare species in there though -- Guam Rail/Kingfisher, Blue-billed Curassow, Brown Kiwi. It also has Lilac-breasted Rollers which are unfortunately being phased out of U.S. zoos.
And also...the National Aviary in Pittsburgh is basically a gigantic version of the average zoo's Bird House, with two walk-through sections, numerous hall exhibits and outside pheasant/raptor enclosures.
I would love to make it to Berlin, Wuppertal, Walsrode and Veldhoven someday. They all sound spectacular.