Afraid of Monsters: a large facility for Monsters is run by two humans: Dr. Henry Hallow (Blue) and Dr. Tib Tigris (Red).
Megatokyo has Largo and Piro, Red Oni and Blue Oni respectively. Erika is also the Red Oni to Kimiko's Blue Oni, though they occasionally switch places.
Sluggy Freelance has Oasis and Kusari, two gymnastic assassins of mysterious origin with superhuman and probably supernatural powers. Oasis is basically insane as a result of Mind Control gone bad, which involved manipulating her emotional states. She is left impulsive and compulsive about the emotional reactions she was ordered to have before her controller was killed and is often incapable of rational thought. Recently, it's even be discovered that she is pyrokinetic, just adding to her fiery repertoire. Kusari obeys orders unfailingly, possibly also mind-controlled, but is still capable of rational thought and always remains cool. The two look about as identical as they can under their respective outfits considering that Kusari is always masked, but Oasis's most noticeable feature is her fiery red hair, whereas Kusari is always shown in the same bluish-purple outfit. There is speculation that the contrast between the two hides symbolism hinting at their as yet unknown origins.
The Continentals: A steampunk murder, mystery, sci-fi, adventure webcomic set in post Jack the Ripper England where Continental Operative Jeffrey Tiffen Smythe is the sophisticated, elegant, intellectual gentleman and his gender bending partner, the adventuress Lady Fiona Fiziwigg, is a hot tempered, foul mouthed, do and say as I damned well please malcontent and proud of it. It's a pairing of mismatched personalities that works surprisingly well as the two investigate a series of brutal "mangling" murders, uncovering a tangled web of intrigue, adventure—and murder!!! Find it here.
El Goonish Shive has Tedd and Susan, sort of. In this case, it's more of a personality difference as Tedd is generally upbeat and unobservant while Susan is a Deadpan Snarker. Other characters lean towards both sides, but generally hover in the middle.
Another notable example is Susan and Diane. A strange case, because they haven't actually met, but they're actually separated-at-birth identical twins who share a few traits but are generally Different as Night and Day. For bonus points, Susan wears a lot of blue and dyed her hair dark blue, whereas Diane's wardrobe is more red and she has naturally blonde hair.
Hanna and Zombie from Hanna Is Not a Boy's Name are a good example: calm, stoic Zombie (Blue) and impulsive, extroverted Hanna (Red).
Also works with a Hot-Blooded, uninhibited Casimiro and disciplined, well-mannered Finas. Even their color schemes are red and blue respectively.
There's also Doc Worth's Jerkass red to Lamont's nice guy blue. Although it's been shown that if anybody can get Lamont to lose his cool, it's Worth.
By the end of Act 5, though, they've pretty much switched places.
Karkat Vantas (red) and Jack Noir (blue) also have traces of this during their team-up in Act V, minus color correlationsnote because trolls think fashion is stupid and Jack Noir is big on black. Karkat is impulsive, loud, and almost always angry at something, while Jack is cool, quiet, and moves with a chilling economy of effort.
Karkat, again, plays Red Oni to John's Blue once they start interacting. Their colour correlations match up as well, and Karkat's first conversation (from his perspective) with John is a textbook example - Karkat is a raging, capslocking, furious, hateful mess, while John responds with a cheerily oblivious "hi karkat!".
Sollux Captor, due to his bipolar mood swings, plays this trope with himself. Later he mellows out and starts playing the blue to Karkat's red.
Juathuur: Dejoru is dark-haired, calm, and compassionate, with the talent to become a healer. Ratheel is loud, fun-loving, has red hair, and fights by making stuff explode. Partly subverted as Dejoru is capable of releasing an enormous amount of raw energy. Ratheel, on the other hand, is completely useless in each and every fight we see.
Quant, the Dark-skinnedFiery Redhead with anger management issues and an egothe size of the Tower. He is too proud to ever openly admit a mistake of his and thus comes up with pretexts when it comes to doing the things he secretly wants to. Like staying with Lero-Ro, his longtime fellow Ranker who once climbed the Tower with him. He is reserved, calm, quiet and patient, unless you start bugging him to much. Unlike the rather Book Dumb Quant he spends a lot of time thinking, especially when he notices that something is going wrong on the Second Floor, which he can't ignore due to his righteous nature (Quant is more of the self-righteous kind). He is also rather sophisticated and a passionate collector of gramophones.
KoonAgeroAgnis and RakWraithraiser, Baam's closest friends in the Tower. The former is a scheming, cheating chessmaster with a lot of brains and some trust issues, the latter a a giantbipedal alligator who just wants to fight, plain and simple, which describes his world view and how he stomps through life, though, unlike Koon, he never lies (though he is a bit of a firendship-type Tsundere for Baam). Koon's color scheme is blue, Rak's is red.
In Girl Genius, we have the upbeat, charismatic Gil and the dour, calculating Tarvek. An interesting example in that they're both Sparks, both schemers by admission, and both part of a Love Triangle with Agatha.
Arguably, Sabrina and Zig Zag from Sabrina Online, the former being a somewhat reserved computer/Transformers nut and the latter an outgoing porn star legend.
Elf Blood has the KO Twins: SKO is the Blue Oni, being an adherent of law, order, and obedience, whereas TKO is the Red Oni, being the runaway renegade with a passion for freedom. Judging from a photograph taken when they were in school, however, this dichotomy may have been inverted in the past.
In Two Guys and Guy, Guy (and occasionally Wayne as well) is the red to Frank's blue.
The Wing Antivirus corporation from Electric Wonderland has modest (blue) Nathaniel Wing as software developer and his meglomaniac (red) wife Nina as CEO.
Kaustos and Two, Heiwa and Nandin, and others from Universal Compass. Almost every character has a foil because they are based off of emotions.
In Next Town Over, John Henry Hunter is a pyrokinetic outlaw with a suave demeanor and a zest for life, while Vane Black is a stoic, melancholic woman who eschews all pleasure and relations in her quest to kill Hunter.
In The Silver Eye Enel is the red oni to Apen Shephard's blue oni, with Enel being the more laid-back and emotionally driven one, and Apen being the more serious and emotionally repressive one.
4Komatose stars Ariake Shikima and Kyushu Miyamoto. Their hair, clothing and even speech balloon borders are red and blue, respectively.
Many examples in The Word Weary, the most obvious being Grace and her room mate, Gary. This is especially evident after she dyes her hair red while Gary's is bright blue. Grace is angry, cynical and open about it, Gary seems calmer and tries to find the humor in bad situations, noticeably after Gary and his boyfriend break up. Other examples include John and Sam vs. Jason and Yorick, and Elly vs. Harry.
Muse, the rather energetic superheroine of Hello Wandering Star is the Red Oni to the Blue Oni of Logo, who believes in the power of meditation.
Nina is Red Oni to Deirdre's Blue Oni in Threading.
In Sticky Dilly Buns, Ruby Larose is (despite her name) basically a lone blue oni in a universe of reds, leading to at least two rough-and-ready, low-key instances of this trope:
She and Dillon are the most obvious case, especially early on in the comic's run. Dillon, the red oni, is a flamboyant Camp Gay man, and is certainly an extrovert with a lust for life; Ruby is a virginal borderline Sour Prude, and is certainly concerned with control and observance of authority, and is also more intellectual, proud, traditional, and definitely introverted, and is a mystery at least to her sister Amber, although she is only intermittently respected. They end up learning quite a bit from each other.
The pattern recurs when Ruby recruits Zii to help her set up a commercial Yaoi fan club, as Ruby has apparently unconsciously recognized that the complementary pairing makes a good business team; red oni Zii has the life experience to judge what will work and useful social connections; blue oni Ruby has the focus and organization to carry through on ideas.
Stand Still, Stay Silent has two pairs. One consists of brash, extroverted fighter Sigrun and quiet, stoic medic Mikkel. The other consists of arrogant Pretty Boy and professional Pyro Maniac Emil and quiet, strangely cat-like scout/mage Lalli.
Alma and her flatmate Edith are Red and Blue respectively - one's ever-excited Genki Girl who takes photos of her desks and speaks with hearts, while the other is The Stoic to such a great extent that one may start to wonder whether she's not an Emotionless Girl.
In The Glass Scientists, vibrant and extrovertic Hyde is, quite obviously, Red, while Jekyll, the very image of British politness, is the Blue.
In Plume, Vesper and Corrick are Red and Blue respectively, with the former a buddying Blood Knight girl wanting an adventure!, and the latter a Seen It AllServile Snarker. The latter even has a blue coat on all the time.
Attley and Fletch, the main characters of The Sanity Circus, respectively form an oni duo. Attley is far more relaxed and active, while Fletch is direct, distant and rushes into things far less readily.