The plots are also remarkably similar if you want to get into spoilers.
Humans live in a big city that isn't the "real world" they think it is and is controlled by seemingly supernatural beings. One human emerges who has the same powers they do and they must stop him. In the process of doing so, one of the beings decides to become more like a human (just like Agent Smith became "like" Neo against his will).
Not only were some of the same sets used, but some of the same shots as well.
Anyway it's an awesome movie so shut it. 
The plots are superficially similar (people A kidnap and use people B in an artificial environment). Beyond the superficial, though, the differences are so great that comparisons break down and claims that Matrix stole from Dark City really utterly fail.
Dark City really seems to be a film noir in which the protagonist follows an increasingly bizarre and upsetting path through a broken narrative toward semi-godhead. Neo follows a fairly straightforward narrative through cyberpunk mythos to semi-godhead.
DC is much more comic book, Matrix is much more movie.
DC has an accidental and unexplained messiah, Matrix has an intentional and, eventually, explained messiah.
The color scheme notwithstanding, the stories are so utterly different that calling one a theft of the other is ludicrous.
