Twin sisters of the Nasu Verse, Aoko and Touko, are this. One is chaotic, the other lawful. Touko was originally depicted as having blue hair until the Kara no KyoukaiOAV gave her an Adaptation Dye-Job to resemble her twin sister more. Genetics beats out symbolism these days. Nevertheless, their Mage Titles are "Red" and "Blue". (Don't bring it up, it's a sore subject.)
Inverted in terms of their titles. Aoko exhibit the traits of red but her title is "Blue" (since the color blue is associated with her magic) and visa versa for Touko. Aoko's name also comes from the Japanese word for blue, "Aoi."
Archer and Lancer of Fate/stay night provide the first Servant duel in the game and are dressed in red and blue respectively. They are often shown battling each other in promotional materials as well as during the UBW intro (they also have a rematch late in UBW), invoking this sort of dynamic. Their colour schemes and personalities traits are reverse, however: Lancer is a hot-headed Blood Knight, while Archer is a cold and calculating Combat Pragmatist and Fallen Hero.
Played straight with Rin and Saber.
Mion of Higurashi: When They Cry has a tattoo of a blue oni, prominently featured in the opening. However, she's far more like the red oni in terms of personality. Then again, the tattoo isn't "hers" to begin with, thanks to an unfortunate Twin Switch in which Shion was supposed to get it. As a result, Mion is supposed to act Red as part of the older sibling role she's forced to play, while her sister Shion acts Blue as part of the younger sibling's role. In truth, Mion's true self is blue while Shion's is red
Keiichi (red) also has this relationship with Mion (blue) to a lesser degree.
In Umineko: When They Cry, Lambdadelta is the red to Bernkastel's blue. In the first half of the series, anyway. In the second half, as their true motivations are revealed, their roles are switched around.
Shannon can be seen as the red to Kanon's blue most of the time, but when it comes to matters of love Shannon is more calm and collected while Kanon is more hot blooded and irritable. It is also heavily implied that they are in fact the same person, and their red and blue dynamic shows Yasu's conflicting views about love.
The Ace Attorney series has some Red and Blue Onis. An inverted example is Phoenix, the blue-clad defense attorney (who isn't as hot-headed as a typical Red Oni, but he doesn't tend to think things through) and his red-wearing frenemy Miles Edgeworth, who is calm, cool, and calculating most of the time. In fact, the lawyers with the more fiery reddish qualities (Phoenix, Franziska, etc.) have a blue motif in their dress, while the more aloof ones (Edgeworth, Godot's visor and clothing as Diego Armando) have a red motif.
Another example from the later game, Apollo Justice, has the title character wearing a red vest - his preference for the color red is even mentioned a couple times in-game - and being rather impulsive (also, his hair is horns!). There are a couple of blue onis in the game. Kristoph Gavin, for one, is, though friendly, very serious and icy as well and wears a blue suit. However, in the end, Kristoph pretty much out-hams every murderer in the series. Klavier Gavin is the epitome of "cool collectedness" and wears a purplish maroon getup.
Also from Apollo Justice, to a lesser degree, we have another inverted version with Klavier in his pinkish/reddish/purplish outfit as a cool straight-man, and his band-mate Daryan Crescend in a blue, shark-like outfit being quite temperamental.
Also played with in Justice For All: Matt Engarde, a popular - if somewhat dim - celebrity wears a scarlet jacket, whereas his manager, Adrian Andrews, is calm and collected and wears blue. In reality, Engarde is a vicious, self-obsessed manipulator and Adrian is a co-dependent, frail woman who's deathly afraid of Engarde.