It really depends on what you want to see, Dallas is much more cosmopolitan as opposed to Ft. Worth which is more traditional. There are more out of the way, touristy "Texan" things in and around Ft. Worth compared to Dallas which is like any other big city.
Downtown and Uptown Dallas both have great restaurants, bars, etc. The downtown arts district is nice as well as the McKinney Ave. area in uptown. The new Perot Museum might be something to check out as well.
Also keep traffic in mind if you're trying to hit a lot in one day, especially if you're staying close to the airport.