Both explore the nature of reality from what may appear to be very different entry points—computers and dreams. But in fact, both movies offer faithful interpretations of Plato's Idealism vs. the Materialism of Democritus.
While Democritus believed physical objects form reality—matter forms mind—Plato believed in "the world as perceived by our senses"—or, mind forms matter.
The backdrop for "The 13th Floor" is the Simulation Theory propounded by Oxford University professor Nick Bostrom and more recently by Elon Musk, who believes without a shadow of a doubt that we live in, and in fact are, a computer simulation run by a future civilization with some serious processing power.
That is to say, our experience of reality is an expression of ideas. Someone else's ideas, specifically. God's perhaps, or the Man Behind the Curtain in the "Wizard of Oz," Or maybe we're just the creations of a zit-faced computer programmer with an exalted sense of self. As Max Plank, the father of quantum theory, put it long ago:
"There is no 'matter' as such. All matter originates and exists only by virtue of a force ... We must assume behind this force the existence of a conscious and intelligent mind. This mind is the matrix of all matter."
The Force and The Matrix in one quote. What's not to love about that?
Meanwhile, "Inception" deals with this notion through the backdrop of dreamworlds and our influence upon them—shaping reality by force of will. As some have put it, the question the movie poses at its climax is not whether the characters are in a dream, but rather, does it matter? It becomes their reality either way.
In "Inception," Leonardo DiCaprio's Cobb explains it this way to Ellen Page's Ariadne:
"In a dream, our mind continuously does this ... we create and perceive our world simultaneously, and our mind does this so well that we don't even know it's happening."
As you'll see, this tension between Idealism and Materialism figures prominently into Rick & Rick's favorite sci-fi movies.
RICK & RICK: TOP 10 FAVORITE SCI-FI MOVIES PART 2: REALITY BITES
(Approx. 5 mins, 14 sec)