Kori Kombat

Tanuki and Kitsune: as far as appearances go, these yokai couldn't be more different. On one hand, tanuki are chubby raccoon creatures with humongous testicles that they can ride on. Kitsune on the other hand, are slender, graceful fox-like spirits that are usually squinty-eyed and possessing anywhere from one to nine tails.

But surprisingly, they have a lot in common: both yokai are shapeshifters with a mischievous streak. Tanuki tend to skew towards being playful, often using their magic to trick humans into taking worthless "money" made of leaves or turning into wine bottles that will continuously roll away from whoever's hoping to take a drink. Kitsune however can be a lot more malevolent, with some of the most dangerous ones such as the Tamamo-No-Mae being known to disguise themselves as or possess women, and use their feminine wiles and magic to bring entire kingdoms and countries to ruin by seducing and corrupting their rulers.

So it should come as no surprise that thanks to the similarities between these creatures, Japanese media often portrays them are rivals or bitter enemies. There's even a name for when these two tricksters fight called Kori no Tatakai (translates to Battle of Tanuki and Kitsune), with the word Kori (狐狸) coming from the kanji of kitsune (狐) and tanuki (狸) coming together as one. But this is no ordinary battle, and instead of a violent clash they have a showdown with their shapeshifting powers as a demonstration of their magic. When comparing the two, kitsune usually overpower tanuki through sheer magical strength, but tanuki are more creative when it comes to their trickery and deceit.

When this trope is in play, expect to see it materialize in several forms: along with the classical battle of wits, sometimes it's as simple as kitsune and tanuki-themed characters beating the crap out of each other. Other times, it's an even more mundane rivalry or a simple contrasting of traits between friends. But as a rule, characters with traits related to these yokai are usually paired together or at the very least serve as distinct foils to one another.

Compare to Fur Against Fang in fiction derived from European folklore.

Examples of Kori Kombat include:

Anime and Manga

Naruto and Gaara were originally enemies as a reference to this trope, with both boys serving as the hosts to Kurama and Skukaku of the Tailed Beasts respectively. They've since become friends shortly before the timeskip and beyond, but Shukaku still doesn't like Kurama thanks to his inflated ego stemming from having way more tails than him.
Averted with Ponchi and Konchi, from Shaman King, most likely due to being Guardian Ghosts to their Shaman.
Pom Poko has an example of how the kitsune have hidden amongst humans and integrated into their society, while the tanukis prefer to live in the forest despite the threat of urbanization.
Subverted in BNA: Brand New Animal with Michiru Tanuki and Nazuna Kitsune. The two girls have been human until recently and transform into Beastmen. Both of them have similar shapeshifting powers while also showing similarities to the yokai of their surnames. They start with a rocky relationship when they meet each other in Anima City, but eventually spend time together and rekindle their friendship.
In Ugokie-Ko-Ri-No-Tatehiki (translates to Moving Picture - Fox vs. Tanuki, Pulling Pranks), a tanuki father and son work together to scare off a kitsune disguised as a samurai from the temple the younger one lives in.
In Gugure! Kokkuri-san, Kokkuri-san (a kitsune) acts as a legal guardian for Kohina. He has a strained relationship with the tanuki, Shigaraki, who is quite troublesome as he often gets drunk, gambles, or causes trouble in other ways.
In The Rising of the Shield Hero, there is a race called Demi-Humans, humans with bestial traits. The two races of Demi-Humans of the Kitsune and the Tanuki both specialize in illusion magic. In the past, the Tanuki managed to seal the Kitsune's great Yokai through deception and sorcery.
Kitsune no Yomeiri has an event between tanuki and kitsune as a prank war every year where two representatives prank random people, and a winner is determined by who punked the most people. The main heroine, a kitsune, is chosen as the representative to compete with the tanuki's representative.

Oral Tradition, Folklore, Myths and Legends

In Japanese folklore, the Kitsune and Tanuki have been rivals since ancient times; whenever they do battle, it usually results in a combat of magical powers and to see who can outwit and outdo the other.
- Especially when Danzaburō Danuki meddles in, also in part, because he made Sado Island into a Tanuki paradise, kingdom, and sanctuary.

Video Games

Referenced in Samurai Warriors with Ieyasu Tokugawa associated with tanuki and his rival, Mitsunari Ishida, related to kitsune.
As seen in the video above, Tom Nook and Redd, from the Animal Crossing series, are both based on a tanuki and kitsune. They were once business partners, but their methods contrast each other. Tom Nook often may trick others with fast talk into paying for products and houses but are functional wares. Redd, on the other hand, lies to sells his wares while grifting them when he gets the chance.
In Kirby's Dream Land 3, Pon and Con are a tanuki and a kistune respectively. But instead of fighting each other, they're fighting against you and serve as a Dual Boss in the vein of recurring Kirby villains Mr. Shine and Mr. Bright.
In Super Mario 3D Land, Mario gets a Tanuki suit when he touches a Super Leaf as one would expect, but when Luigi touches one? He gets a kitsune suit instead that functions exactly the same (wagging their tails to slow their fall, allowing them to make some impressively long jumps). While they deeply love each other, the RPG's and a few sports titles show that there's definitely a healthy bit of Sibling Rivalry going on between the two.
Touhou has the Tanuki-based Mamizou Futatsuiwa and the Kitsune-based Ran Yakumo, who utterly hate each other's guts. Playing on an old Japanese myth, Mamizou is even meant to be a stand-in for Danzaburou of legend and is responsible for kicking out all the foxes from Sado.