While most of the characters tend towards red oni, Red vs. Blue has a bit of this going on in the different teams, mostly their leaders. Church, the man in charge of the blue team, is fairly on-the-ball and tries to get things done, and he took over from Butch Flowers, a soft-spoken, thoughtful man whose only flaw seemed to be in thinking that the whole Red Army versus Blue Army conflict was something of a game and strategizing accordingly (in a flashback, when Church reports on Red activity, Flowers refers to them as "Those rascals!" in a no-hard-feelings sort of way). Sarge, leader of the red team, puts exactly no thought into his battle plans beyond how they can be used to kill Grif, but he goes at them with such a fervor that, if he did think about his plans for three seconds straight, he might actually win.
On a more individualized level, the Freelancer Dakota twins. North is the Blue Oni—calm, cautious, and strictly by-the-book during missions, and rather mild-mannered and friendly during downtime. South is the Red, a hasty, Hot-BloodedLeeroy Jenkins during battle, and bitchy, abrasive, and almost anti-social the rest of time.
Also, Blue Team tends to be the origin of most of the show's drama and plot while Red Team tends to just provide the slapstick and comedy.
Furthermore, the Chorus Arc introduces us to Felix and Locus, a pair of mercenaries who form their own Oni Duo. Felix is the Red Oni, being sarcastic, higher-energy, and generally more frivolous. Locus is the Blue Oni, being calm, quiet, and almost obsessively mission-focused.
Gantz Abridged actually calls this trope out in a full-on Shout-Out to the TV Tropes Wiki, with an actual Red Oni alien telling a Green Oni alien that he's supposed to be Blue and asking if they're subverting the trope. The trope is then furthered carried out when the Red Oni decides to immediately resort to smashing things, to which the Green Oni replies, "You WOULD say that."
And in hbi2k's earlier work, Berserk Abridged, Zodd compared Guts and Griffith to Naruto and Sasuke. Griffith however believed that Guts should fulfill the Sasuke role since he's the angstiest of the two.
DesuDesBrigade has the two female-presenting reviewers JesuOtaku and Vixen to match up to this trope. While Vixen is the more emotional and tends to freak out more often (see: Papa To Kiss in the Dark), JesuOtaku is far more reserved and analytical. The same goes for Professor Otaku and Arkada, though not nearly as stark of a contrast.
The Mondo Media series Dick Figures features a red stick man and a blue stick man with distinctly opposite personalities.
In Everyman HYBRID, HABIT and The Slender Man come off this way, especially in the fights between the two on Twitter. (Yes, Slender Man actually says something. It's actually pretty creepy.) HABIT types in ALLCAPS and is absolutely insane and unambiguously evil. Slender Man seems condescendingly amused by his shenanigans and his messages are typed normally.
Before HABIT's nature came to light, The Rake was typically thought to be the Red Oni instead.
When Po Ping and Tai Lung arrived in Ink City at the same time, both ended up on the Paint Side of the currently split City and wound up temporarily recolored in the spirit of this. Po found his black and white replaced with vibrant shades of red and yellow and deemed his unexpected makeover awesome. Tai Lung, on the other hand, finds his fur turned various shades of blue and was considerably less amused.
Kyle from Statless And Tactless is the level, balanced player to Joe's sociopathic antics. They even have blue and red text.
Trunks2585 has an example in Xander's Reviews. Xander is emotional and gregarious, while Alejandro is logical and reserved. This counts as an inversion, because Xander wears cool colors (usually green), and Alejandro wears warm colors (usually orange)
Slowbeef is often more expressive, whether it's getting angry at the creators of the video or game they're mocking or laughing more at something unintentionally funny in it. Diabetus, on the other hand, is more of a laid back Deadpan Snarker.
Likewise, Chip Cheezum is excitable (though usually less angry than Slowbeef), while General Ironicus tends to be more calm and, like Diabetus, more of a Deadpan Snarker.