Both films take place in the same neo-trash, dark cities. And by same, we do mean the literal same.
See, what Hollywood likes more than anything is not having to pay for more crew than needed; why hire someone to make a set when you've got a perfectly good one lying around in storage? So when the Wachowski Sisters were looking to make their sci-fi rip-off of a crazy Scot's comic, they went ahead and reused some of the Dark City sets..
New Line Cinema, Warner Bros.
Now, unfortunately, both Dark City and The Matrix, in addition to being set in the same city, have similar themes -- a man in a city alone searching for answers, discovering the truth is darker and more horrible than he could possibly have believed. In one, it's aliens; in the other, his body is in a jar being fed liquefied dead people, while giant robots try and eat his energy (because the original concept was supposedly worse).
Is the alien stuff all a cover for the dark truth behind the city? Are the aliens just what Agent Smith does on his days off? Is this another one of the Machine cities, but with a built-in backup story for why shit's all messed up, so no one realizes? Are both films secretly set within the Thirteenth Floor?
Either way, when you see Trinity running over rooftops, spare a glance for Rufus Sewell hunting down aliens below. God, The Matrix would've been so much better if after Neo said he knew Kung Fu, Morpheus went "Now for telekinesis."