There are a fair amount of depictions of Cresselia and Darkrai as rivals, but to be honest I feel like that angle is kind of boring from a character perspective, as it just falls into the standard "evil creature is always evil and good creature is always good" trope.
Conversely, the other way to depict them is as allies, which is a more interesting take. Darkrai (at least in the mainline games' continuity) does not want to hurt anyone. It makes sense that, while it might be envious of Cresselia, it would also be grateful that her abilities work as a hard counter to its own.
However, while there isn't any real basis for this, I like to take it a step further and think of the two as being hard counters to each other. Cresselia's good dreams are wonderful, and help to ensure deep REM sleep—so deep, in fact, that it can accidentally overdo it and lull people into a borderline comatose state by giving them dreams so good they don't want to wake up. The fix? Darkrai showing up and inducing nightmares in order to force the person awake.
This creates a more ying-and-yang dynamic between the two. Cresselia balances Darkrai; Darkrai balances Cresselia. You can't have the night sky without the moon; you can't have the moon without the night sky. Does this make sense to anyone else or do I just sound insane