Two gods quarrel about rank and a third settles it. Between Brahma and Vishnu rises a shaft of fire with no visible end. Vishnu, as a boar, burrows for its root and comes back honest: he could not find it. Brahma, as a gander, climbs for its crown, meets a ketaki flower drifting down from far above, and persuades it to swear that he plucked it at the summit. When Brahma repeats the claim, Shiva appears from the column, names the lie, and lays down two rules: no one in the three worlds will worship Brahma, and the ketaki will not be used in Shiva's worship, though the same chapter lets it hang above his canopy.
On Shivaratri, north and south alike, the same story is told to explain a rule of worship: the screwpine flower is left out of the offerings because it once lied for Brahma.
What is different here:
Used as an etiology for the ketaki taboo rather than as a story about Brahma's worship.
The temple's literary tradition sets the column of fire at Arunachala itself: the hill is the pillar cooled into stone. On Lingodbhava day and at the climax of the Karthigai Deepam festival a great ghee lamp is lit on the summit to stand for the light that Brahma and Vishnu could not measure.
What is different here:
The pillar becomes the Arunachala hill and the story gains an annual festival; the Chola temples carve Lingodbhava on the west wall with Brahma as gander above and Vishnu as boar below.
Sources: True meaning of Mahashivratri — Bhavam Bhavaani; Battle between Brahma and Vishnu (Shiva Purana) — VedicFeed; Lingodbhava — Wikipedia; Things to avoid on Maha Shivratri — Svastika; Karthigai Deepam — Wikipedia