Digimon Savers: In their burst mode evolutions Masaru powers up by summoning a miniature sun and dropping it on himself, while Thoma powers up by summoning a crescent moon.
In Rurouni Kenshin: Kenshin and the Kyoto arc Big Bad Shishio Makoto can be considered rivals (both were highly skilled hitokiri during the Bakumatsu period (1853-1868), and now they're enemies. In their final battle, Kenshin's revamp and secret attack summons forth a fierce squall, while Makoto's special attack and power up are announced by roaring flames.
Rin Natsuki/Cure Rouge and Karen Minazuki/Cure Aqua from Yes! Pretty Cure 5. The former uses fire elemental magic and is designated as the Cure of Passion. The latter uses water elemental magic and is designated as the Cure of Intelligence. These two characters early on are depicted as rivals that couldn't get along most of the time and hate being one-upped by the other. However, over the first season, they came to an understanding, and the rivalry became less severe.
Discussed in Freddy vs. Jason where it's suggested that some of the animosity between Freddy Krueger and Jason Voorhees stems from the fact that the former was created from fire, and the latter was created from water (Freddy became a dream-dwelling demon after being burned to death by an angry mob, and Jason became a hulking zombie after drowning as a child).
Generally speaking, almost every religion will associate the Big Good god with Light or Sun or the Heavens, while the Satan character of God of Evil will be associated with Darkness, Night or Earth (namely the Underworld]].
The four Elemental Lords of the Forgotten Realms setting each hate the one that embodies their opposite element. Akadi the Lady of Air battles Grumbar the Earthlord, and Kossuth the Firelord duels Istishia the Water Lord.
Warhammer and Warhammer 40K: The four Chaos Gods are opposed two by two, as they are essentially the sum of one emotion felt by sentient creatures. Khorne (rage) is opposed to Slaanesh (desire) and Tzeentch (hope) is opposed to Nurgle (fear of death).
Most Toa teams in BIONICLE have a Toa of Fire as The Hero and a Toa of Ice as The Lancer, typically having a Red Oni, Blue Oni dynamic. Tahu and Kopaka are the most prominent example, although they're both just as likely to start arguing with Gali, the Toa of Water, as they are with each other.
Samurai Warriors has Kenshin (ice) and Shingen (fire), Yoshihiro (wind) and Ginchiyo (thunder) and also Nobunaga (wind) and Mitsuhide (thunder). Note that in most cases it refers to the chosen element of their ultimate weapon.
Mitsunari (darkness) and Ieyasu (light) in Sengoku Basara. It also has the duo Kenshin (ice) and Shingen (fire) as tamer rivals.
Onimusha: Dawn of Dreams has the Genma God of Light (Fortinbras) opposed to the Oni God of Darkness (Soki).
Prince of Persia The Forgotten Sands has the elemental opposition between Razia the Marid Queen (who has powers over water, which in the series symbolize life) and the Ifrit Lord Ratash, who has power over both fire and sand (which, in the series, is opposed to water as a symbol of death and entropy.)
Dark Dawn: Two gems that give you the power to evaporate water or turn it to ice are held by the Sand Prince and the Frost Queen. The former is a Worthy Opponent who battles you to gauge your strength before he willingly gives you the gem, the latter is a textbook evil queen who won't give up her gem peacefully.
Somewhat indirectly we have Raze and Ulrika, who got their powers from the Light Mana and Dark Mana respectively. Indirect because while Raze is a truly Light 'em Up guy, Ulrika is more like Soul Power. The real Casting a Shadow person is Ulrika's best friend, Chloe, who doesn't have much interaction with Raze otherwise.
There is also some sort of rivalry between Whim and Yun, being a Water Mana and Fire Mana respectively.
In Touhou, we have Kaguya Houraisan representing the Moon and Fujiwara no Mokou representing Sun. While Kaguya's actual powers don't have much to do with the Moon, she is a Lunarian. Mokou meanwhile has a lot of The Phoenix theme going on.
In Adventure Time Flame Princess ( fire elemental ) sees Finn crying over her. She thinks he's a water elemental because he "releases water," which is why they can't get along.
Five hats means that five tropers think it is ready to publish.
You are saying that you think this draft is ready to be published. That means the description is not ambiguous,
it doesn't duplicate an existing trope, there are at least three examples, and the title makes sense.
Is that what you meant to do?
You are saying this draft has a ready-to-publish hat it does not deserve and you are taking it back.