Visitors to the new Chanel exhibition at the Metropolitan Museum of Art might be forgiven for thinking that they are ringside at a catfight between two prickly, preening fashion personalities rather than browsing a museum show.

In one corner is the modernist Gabrielle Chanel, better known by her nickname Coco, who liberated women from constrictive corsets, ruffles, and frills, launching them instead in little black dresses of silk crepe, tulle, and even jersey, a fabric that had been previously used only for men’s underwear.

In the other corner is Chanel’s current impresario, Karl Lagerfeld, whose updating of the French lineage has made the house a bastion of blue-chip chic. Yet many critics have carped that “Kaiser Karl” has in the process undone his predecessor’s work on behalf of modern women. (At least one of Mr. Lagerfeld’s collections required that women don a corset – the Victorian contraption Coco so defiantly eschewed – to fit into that season’s iteration of the Chanel suit.) Quotes from both Chanel and Mr. Lagerfeld are printed on the walls throughout the exhibit.

The two personalities seem most opposed in their concepts of how clothing figures into the Now. Said Chanel: “I do not like when one speaks of the Chanel fashion. Chanel is first a style. Fashion passes … style remains.”

Mr. Lagerfeld, meanwhile, pounces on the trendy. This is the man, after all, who brought us the Chanel surfboard and the Chanel moon boot. (Even Mr. Lagerfeld’s weight has fluctuated by the decade: This month marks the release of a book promoting his own fad health regime, “The Karl Lagerfeld Diet.”) “I like today,” Mr. Lagerfeld declares. “I am not interested in the past.” So opposed was the forward-looking Mr. Lagerfeld to the idea of a museum show that the Met’s first attempt at a Chanel exhibit, two years ago, was scuttled over creative differences. Mr. Lagerfeld was pressing for a show of contemporary art instead of a retrospective of “old clothes”; the multimedia projections that pepper the current exhibit are surely concessions to Mr. Lagerfeld’s desires. (Chanel, despite Mr. Lagerfeld’s professed lack of involvement in the exhibit, is a major sponsor of the show.)

Mr. Lagerfeld’s objections to the idea of a Chanel show have the effect of exonerating him from charges of self-promotion. Placing Mr. Lagerfeld’s designs from the 1980s, ’90s, and the current decade next to the legendary Chanel originals, as the Costume Institute’s curators Harold Koda and Andrew Bolton have nimbly done, might have drawn complaints of sacrilege – were it not Mr. Lagerfeld himself doing the complaining.

The inclusion of Mr. Lagerfeld’s designs is likely to please the Met’s patronage, who can look on his “scuba” versions of the Chanel jacket (Spring/Summer 1991) and bask in the knowledge that they have their own “museum piece” hanging at home in their closet.

And the juxtaposition between Mr. Lagerfeld’s and Chanel’s pieces reveals the stunning achievement of both designers. If the armature of the exhibit positions Mr. Lagerfeld as almost contemptuous of the Chanel mystique (which just goes to show how well matched the two designers are in their irreverence), the actual presentation of the clothing shows the two artists in a deep and lively dialogue.

In the first few “vatrines,” as the minimalist white boxes holding the exhibit’s display mannequins are called, Coco Chanel’s clothing is presented front and center, with Mr. Lagerfeld’s contemporary versions arranged in the background, like ghosts or shadows. It’s an almost lyrical gesture, reminiscent of Matthew Bourne’s recent ballet, “Play Without Words.” The mannequins themselves, with their witty feather headdresses by Odile Gilbert and attenuated, Virginia Woolf-like visages, give the fashions a similar poetic grace.

But after this early detente, the curators intermix the two designers’ clothing to the point where Mr. Lagerfeld’s and Chanel’s designs grow indistinguishable. I had judged an Empire-waisted silk lace frock that points out around the knees to be a gorgeously preserved Chanel original, only to find that it was Mr. Lagerfeld’s couture work, circa 2004-05.

Meanwhile, a gold satin sheath that is exactly what Hollywood sirens long to wear down red carpets turned out to be vintage Chanel, circa 1928. Because Chanel was foremost a proponent of simplicity in dressing – owing, no doubt, to her schooling in a convent – and because she brought the rigor of menswear and the uniform into women’s wardrobe, her designs already look like postmodern riffs on classic themes.

If Mr. Lagerfeld is an uncannily skilled interpreter of the past – his objections to the contrary be damned – it’s fortunate that he had such a modern and rich legacy to inherit. When Chanel said “style is eternal,” she was not speaking in generalities. She was both specific and prescient. It was really the Chanel style she meant. And she may very well have been right.