I have visited both zoos, and I would have to say that I preferred Dallas zoo for a number of reasons. First and foremost as an Australian, Dallas zoos collection of Birds, reptiles and mammals from this region (Australia/New Guinea) was very, very impressive. I saw so many things that I had never even seen in an Australian zoo. It was so impressive in fact I actually asked if there was a specific reason or intent behind it (their answer was basically 'dumb luck' - zoos apparently pick up spare animals or exchange them at random). The rest of the zoo was world class as well, including the safari train ride, a bird house, penguin exhibit to name but a few.
Anyhow, I was far less impressed by Fort Worth zoo, albeit I did see it during the beginning of winter and I went to Dallas during high summer. The Australian section was woeful in comparison, and the parrot exhibit (they are easily my favourite birds) was closed. There were a couple of nice water bird exhibits, some massive fish to feed and a wild west town of sorts (for the tourists I guess, but certainly did nothing for me). The two highlights for me were (and again remember I am an Australian, albeit married to a Texan) was the New Guinea Crowned Pigeon (just such a spectacular bird), and a believe or not a talking Bird of Paradise. It's vocabulary includes 'hello there' and 'beautiful boy' plus hysterical mumbling to himself, which sounds like he is saying something, but you can never quite make out what it is (and it definitely was human talking not bird noise). Plus he'd come up to the cage wire as he was fascinated by people. Birds of Paradise come from Australia and New Guinea but I had never heard that they could actually talk, so I discovered something that was quite amazing at Fort Worth Zoo.
Finally don't forget Dallas Aquarium. Again world class and has much, much more to look at then simply fish. You'd amazed how a place that looks so compact from the outside can seem to go on forever. It will certainly take up most of your day.