Turner or Constable: who’s the boss? Tate Britain’s exhibition of work by the two artists, subtitled Rivals and Originals, fudges the question. Born a year apart and both alumni of the Royal Academy schools in London, each was keenly aware of what the other was doing, in a British art world that was as febrile and competitive, if immeasurably smaller, than it is today (although you should try the Italian Renaissance if you want full-blooded rivalries and enmities). Sometimes, they sought the same collectors and painted the same subjects. Turner was encouraged from an early age by his father, a Covent Garden wigmaker and barber; Constable was the son of a Suffolk mill owner and grain merchant who wanted him to take over the family business.

As well as their contrasting backgrounds, their temperaments could not have been more different. A scene from Mike Leigh’s 2014 film Mr Turner, starring Timothy Spall as Turner and James Fleet as Constable, plays in the show, presenting the two painters bickering on Varnishing Day at the Royal Academy in 1832. Turner added a touch of red, in the form of a buoy, to his seascape Helvoetsluys; the City of Utrecht, 64, Going to Sea in order to upstage Constable’s The Opening of Waterloo Bridge, on which the painter had been working for more than a decade. But whatever their rivalry entailed, it was hardly the odd-couple bromance between Van Gogh and Gauguin depicted in the 1956 Vincente Minnelli movie Lust for Life (Gauguin: “You paint too fast!” Van Gogh: “You look too fast!”). It is worth remembering that Constable once wrote in a letter: “Did you ever see a picture by Turner, and not wish to possess it?”

Turner’s Dolbadern Castle, North Wales, 1800. Photograph: Royal Academy of Arts, London

The last time these two paintings were brought together was at the Royal Academy in 2019, and Helvoetsluys, owned by the Tokyo Fuji Art Museum, is not included in the current show. But we do have Constable’s folding sketching chair and sections of Turner’s fishing rod and a reel as well as various palettes, paintboxes and other paraphernalia belonging to each artist. And painting after painting after painting, watercolours and sketches from throughout their careers.

Compare Turner’s Dolbadern Castle, North Wales, 1800, with its looming tower silhouetted against a boiling evening sky and its allusions to 13th-century struggle for Welsh independence (and the threat of the French Revolution spreading across the Channel), and Constable’s diploma work submitted to the RA 29 years later, which shows a man opening a lock to allow a boat passage upriver. This is a painting of two men and a dog, a view across the meadows beside a working river, some trees, a distant church and a tremendous sky with a passing rain shower. Turner’s painting is extraordinary and portentous, while Constable’s celebrates an everyday, although now vanished world. I can almost smell the river.

A Boat Passing a Lock, 1826, by John Constable. Photograph: Heritage Image Partnership /Alamy

Constable invites the eye to wander from the squelching underfoot to a distant lowland horizon, and to imagine things that cannot be seen as the river bends out of sight. Turner has you cowering in the gloom beneath the castle on its promontory. His “sublime” becomes a predilection for drama and vaporous emptiness, whereas Constable’s paintings are filled with stuff: carts, posts, locks, windmills, cottages, churches, cathedrals, river boats, horses, donkeys, sheep, bargees and people fishing; reeds, burdock, willows, cornfields, hedges, elms, oaks, weather, rainbows and clouds. Constable was drawn to “the sound of water escaping from Mill dams, Willows, old rotten Banks, slimy posts, & brickwork. I love such things … As long as I do paint I shall never cease to paint such Places.”

Turner, who travelled further, gives us mountain passes, wild seas, steamboats and coal barges and the atmospheric pollution of London and the Black Country. He paints the burning of the Houses of Parliament, disasters at sea and incomprehensible painted storms. He painted Noah’s ark on the evening of the deluge and a mashup of Goethe’s theory of light and colour with Light and Colour (Goethe’s Theory) – the Morning after the Deluge – Moses Writing the Book of Genesis, depicting Moses sitting in a sort of bubble, floating in the ether. Turner paints figures that are as inept as those of his beloved Baroque landscape painter Claude Lorrain. Turner’s all over the place. His 1832 Staffa, Fingal’s Cave, has the sun like a billiard ball resting on the horizon, the basalt rocks far on the left picking up the last rays, as the rain moves through, along with the steamboat’s trail of smoke. This is great, but then he goes and paints The Golden Bough, an absurd concoction with figures in a hazy landscape, and decorous pines planted hither and thither, and the little votive sculpture in its blue niche in the rock.

JMW Turner, Keelmen Heaving in Coals by Moonlight, 1835. Photograph: Studio A/National Gallery of Art, Washington, Widener Collection.

When Turner paints Snow Storm: Hannibal and his Army Crossing the Alps in 1812 he pictures Hannibal sitting on his elephant on the horizon, a tiny detail in the huge canvas. The distant animal, with its trunk raised, looks as threatening as a teapot. And what of the lumpen extras in the bottom right-hand corner? It is like a high fantasy CGI scene from a movie, more Lord of the Rings than Gladiator, though Turner was thinking of Napoleon Bonaparte, who was often compared to Hannibal. I gawp but don’t care. Where’s my popcorn? Even the title reads like a bit of superimposed text in a movie.

Turner liked the specificity of the titles he gave some of his more grandiose, clamorous scenes. They lent a certain veracity to all that painted chaos. In 1842 he painted Snow Storm – Steam-Boat Off a Harbour’s Mouth Making Signals in Shallow Water, and Going By the Lead. It is inscribed: “The Author was in this Storm on the Night the Ariel left Harwich.” We are lost amid the brown filth from the smokestack, the spume and snow, and heaving sea, the flag signalling how lost we are. Somehow, we have to negotiate all this. When he is specific, Turner is great.

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Turner’s Fishermen at Sea, exhibited in 1796. Photograph: Courtesy of Tate

Constable is always specific, grounded, even when he is just staring at the clouds or into the impenetrable dark on a heath, the moon half seen emerging from behind a bush, in its pale bloom of scattered light. Another contemporary, the German Romantic painter Caspar David Friedrich might have coveted this little scrap of unstretched canvas. Constable’s skittering, glittering highlights in his later paintings, those little scrapes and spots and flecks of white that seem detached from any object aerate his worked and reworked canvases and make something entirely fixating of the passing world.

Hampstead Heath With a Rainbow, 1836, by Constable. Photograph: Tate

But this feeling was already there in Constable’s cloud studies, painted in the early 1820s. Birds wheeling, clouds billowing and sagging, layered banks of greenish, greyish and bluish cloud, clouds flaring and underlit by the setting sun, rain-heavy clouds and others almost dissolving, clouds with luminous edges and clouds reduced to a few pattering, indistinct marks, massing in gradations of lighter and darker touches. I prefer these small and almost casual studies (yet how specific they are!) to almost anything else in the entire exhibition. They feel suspended in the here and now as much as they record a particular day almost 200 years ago. At his best, Turner could be just as exact, especially at his most offhand, but Constable touches me more.

Turner & Constable: Rivals & Originals is at Tate Britain, London, 27 November to 12 April