James Ellroy seems to love this trope; the two detectives at the center of his The Black Dahlia are even referred to explicitly as Mr. Fire and Mr. Ice.
The Will Ferrell movie Blades of Glory has Chazz Michael Michaels, the improvisational, womanizing idiot, and Jimmy MacElroy, the technical, thoughtful man-child Blue Oni. This is even reflected in their "Fire and Ice" costume.
Every Die Hard movie has one or more elements of this. John McClaine, the hot headed runner and gunner always goes up against a calculating intellectual Big Bad. The first two movies also have a subplot involving McClaine's "Red" tactics budging up against the "Blue Oni" by-the-book style of the authority.
Fight Club: Tyler is impulsive and rash, whereas the Narrator is a calm and cool corporate executive. Their different personalities are, of course, all mixed-up in the heat of the fight.
Hard Core Logo has the intense, impulsive Joe Dick and the quieter, more calculating, ambitious Billy Tallent.
In the Hellboy series, the title character (sloppy, hot-tempered demon dating a human flamethrower) and Abe Sapien (studious, slightly prissy gillman) are actually addressed as "Red" and "Blue" respectively; although this is due to, y'know, their actual skin color, the association still fits. Hellboy and Krauss, too, particularly when Krauss is posessing that Golden Army trooper in the final scene -- all his glowy bits go blue. They fit the personality portions of this trope to a T.
In the movie version of L.A. Confidential, Edmund Exley is a near-perfect example (who nearly always dresses in a blue suit to boot), while Bud White is very much a Red (complete with brown/maroon suit).
In the film characterization of Lord of the Rings, there's the angry dwarf Gimli and the elegant Legolas.
In Men in Black, Agent K is the serious, deadpan Blue mentor while Agent J is the wisecracking, impulsive rookie.
The classic French musicals, Moulin Rouge and The Phantom of the Opera display similar themes of love, business and obsession between one another. However Moulin Rouge aims towards modern and frankly grotesque love themes, while The Phantom of the Opera is a lot more traditional and subtle.
Osmosis Jones has this with a color inversion. Ozzy fits the Red mantle and Drix the Blue mantle. This is despite Ozzy being blue and Drix being red.
The Sith and the Jedi fits this trope to a T. The Sith wield red lightsabers and are defined by their passions and their ambitions. The Jedi typically wield blue or green lightsabers and are presented as more intellectual and steeped in tradition.
On a more individual level, the master/apprentice relationship between Obi-Wan Kenobi and Anakin Skywalker during the prequel trilogy. Obi-Wan is the more cautious and thoughtful blue Jedi and Anakin, being younger and more ambitious, represents the passionate red. Of course, this speaks volumes about the paths the men choose by the end of the end of said trilogy.
Franchise-wise, the prequel trilogy is the Red Oni to the original trilogy's Blue Oni.
However, the sequel trilogy can be seen as the Red Oni to the prequel trilogy's Blue Oni.
The Force Awakens is the Red Oni to Rogue One's Blue Oni.
Director Krennic is the ambitious, self-promoting Red Oni to the stern, cold-hearted Grand Moff Tarkin's Blue Oni.