Anime Tropes: Red Oni, Blue Oni
The "Red Oni, Blue Oni" is a way in which (mainly) Japanese works of fiction portray duality by contrasting two characters with opposing personalities. Sometimes, the characters are rivals, but more usually, they're teammates who sometimes get on each other's nerves, because their personalities are so different.
The concept comes from Japanese folklore. The interesting thing though, is that because there is narrative potential in this kind of characterization, it has become common in the West sometimes as well. By narrative potential, I mean it has the potential to create conflict, as two allied characters can have different approaches to situations based on their personalities.
In Jungian personality psychology, the "red oni" is a feeler and the "blue oni" is a thinker. The "red oni" leads with his or her emotions, the "blue oni" is more reserved and logical. This duality is seen in many characters and it quickly becomes a pattern you can recognize in a lot of anime, but also in Western media.
A red oni/blue oni pair of characters is often shown by color palette or elemental magic, with the red oni character being prone to red or orange costumes and fire-based magic, while a blue oni character will have blue or purple costumes and ice or water-based magic. However, this is not always the case. For example, Roy Mustang is something of a "blue oni" for Edward in Fullmetal Alchemist, despite having fire-based magic. What really matters is the characters' personalities.
Rei and Asuka, Evangelion
Natsu and Gray, Fairy Tail
Mugen and Jin, Samurai Champloo
Vash and Wolfwood, Trigun
Rei and Usagi, Sailor Moon
Elsa and Anna, Frozen
Megamind and Metro Man, Megamind
Batman and Superman, DC Comics
Scarlet Witch and Quicksilver, The Avengers (and other Marvel Comics)
The Breakdown: A Chart
Slow to Act
Detemined to Win
As you can see, this trope is used a lot in anime and in other media to show that characters have opposite personalities. This is interesting in a narrative because it creates characterization by contrast. But, it can also become something of a cliche, making the characters behave in patterns that are predictable and therefore dull.
Like any trope, it can be done well if it is subtle and innovative, with the creator putting their own spin on it. And, as with other characterization tropes, it's important that your red/blue characters are something other than just red or blue characters. It's essential that characters feel organic, like real people with real identities that go beyond copying generic character types.
For example, Elsa in Frozen, who is much more emotional than other 'blue oni' examples, but is therefore more believable as a person, not just living out the 'blue oni' character type to the letter. Creators can use this trope, but not to the point of it making their characters into predictable cliches.
Characterization tropes should be seen as guidelines, not cookie cutters.