http://galeon.hispavista.com/cinerama/actu2/matrixdarkcity.htm site is in spanish, but it has plenty of pictures...
Ebert called The Matrix a "poor man's Dark City." I can see why after looking at some of the shots. I don't think there is any doubt that the director of The Matrix used Dark City as a refrence for his movie; too many similarities to be otherwise. Both great movies, one fed on the horrors of the city and the other consentrated more on the "resistance."
I noticed as I was watching it in the theater that The Matrix bore a striking resemblance plotwise to Dark City. The only difference was the latter didn't have the kung fu and gunplay(which would account for the huge disparity in box office gross). Then again, a lot of similarly-themed films came out around that time. Dark City, The Matrix, eXistenZ, The Truman Show, and Open Your Eyes(Abre Los Ojos) all dealt with the idea that the life the main character is living may not be real. And as far as Dark City and The Matrix looking the same, that's partly because some of the same sets were used for both films.
Both of these movies were produced by Andrew Mason. Mason addresses similarities between the movies in an interview at The Matrix website.