Americans seem to thrive on rivalry. And we like winners and winning. We also want to be heard. During the 1940s and ’50s, when the avant-garde artists of New York supplanted those of Europe, Abstract Expressionism and the New York School were celebrated as having literally “triumphed” over the School of Paris. American “Action Painting” and its mural scale, it was believed, had displaced the European easel picture and its centuries-old view of painting as a window on the world. America — specifically the New York School — which had taken the next big and inevitable step in the visual arts, became the reigning center of the art world. A show at the Jewish Museum, “Action/Abstraction: Pollock, de Kooning, and American Art, 1940-1976,” which focuses on the art, ideas, and people who defined those shifts, revolves around the rivalry between that period’s two most vocal, powerful, passionate, and influential art critics — the Jewish intellectual adversaries Clement Greenberg (1909-94) and Harold Rosenberg (1906-78).

“Action/Abstraction,” organized by Norman Kleeblatt of the Jewish Museum, Douglas Dreishpoon of the Albright-Knox Art Gallery, and Charlotte Eyerman of the Saint Louis Art Museum, is generally a sound, if somewhat questionable, exhibition. It rounds up works from across the country and includes, among its 50 artworks by 31 artists, some first-rate pictures and sculptures, as well as, in its “context” galleries, a very strong and elegant grouping of mid-20th-century graphic design (show catalogs and posters) and some interesting period artifacts (don’t overlook the Life magazine articles, the letters written by artists, including Clyfford Still, to Greenberg and Rosenberg, or the jigsaw puzzle of Jackson Pollock’s painting “Convergence”).

The first gallery, with four works by Pollock and three by Willem de Kooning, is stunning. The largest painting in the compact room, at nearly 13 feet across, is “Convergence” (1952), which spreads across the end wall. Pollock’s painting is a full-frontal assault. Its linear reds, yellows, blues, and whites are interwoven and held within a matrix of black. And its unprimed off-white canvas ground, competing with the artist’s poured, dripped, and flung web of paint, presses forward with equal intensity, vying for frontality. Also on view are Pollock’s “Totem Lesson 2” (1945), in which animistic forms feel embedded within a blue-gray ground; Pollock’s beautifully milky, inky black-and-white enamel “Number 9, 1951” (1951); a burly De Kooning “Woman” (1949-50) in yellows and violets, as well as De Kooning’s iconic works “Gotham News” (1955) and “Black Friday” (1948), a mostly black-and-white painting as arresting for its looping insouciance as for its taut, planar architecture.

But also on view in the initial gallery (and the first actual works to greet viewers) are two dueling films of Pollock and De Kooning applying paint: De Kooning putting brush, wet-into-wet, on one of his “Women” and Pollock pouring paint onto a canvas spread across the floor. We are informed in the wall text that Greenberg championed Pollock and that Rosenberg championed De Kooning. Let the games begin. “Action/Abstraction” immediately shifts the emphasis from the art to the artists, critics, press, and the public; from what the art does and why it is worth our attention to the arenas in which the art was made and to the discourses, responses, and rhetoric surrounding the art. Process, competition, and context are the basis for this show in which the artworks are in danger of becoming illustrative backdrops and bullet points for the curators’ thesis about critical reception.

In that sense, the position of “Action/Abstraction,” which is as much an arena as it is an art exhibit, is Rosenbergian, as opposed to Greenbergian. Greenberg was a formalist (a term that, in part because of Greenberg, has become something of a dirty word) who believed in conscious composition and truth to materials. He pushed for flat, pure, handless abstraction that is concerned with a distillation to essences — an allover painting that hits the viewer all at once — epitomized in Pollock’s dripped canvases, and which found its endgame in the work of the Color Field painters (pictures by Mark Rothko, Ad Reinhardt, and Barnett Newman, who are also represented here). Rosenberg, perhaps more of a romantic than a formalist, coined the term “Action Painting,” the precursor to “Abstract Expressionism,” in 1952. He believed the canvas was a spontaneous, intuitive, and existential arena in which the angst-ridden artist acted, letting the composition evolve unpredictably, naturally, dangerously.

“Action/Abstraction” walks us through the artists championed or ignored by Greenberg and Rosenberg. There are some wonderful sculptures here (despite the fact that most are cramped against the walls) by Anne Truitt, Anthony Caro, and David Smith, who Greenberg believed was the greatest sculptor of the 20th century. Hans Hofmann’s “Sanctum Sanctorum” (1962), in which hard-edged rectangles of pure color fluctuate within a red-orange ground, is both fluid and punchy. In a section titled “Anxious Objects,” which includes works by Jasper Johns, Claes Oldenburg, and Philip Guston, Joan Mitchell’s “Untitled” (1957), in wintery blues, bronzes, blacks, and whites, towers over more august company. And there are some revisionist moments (a visually weak section called “Blind Spots,” devoted to Lee Krasner, Norman Lewis, and Grace Hartigan, fails in its attempt to set the record straight).

The show, which touches down briefly into the territories of representational, Pop, and performance art (movements championed by neither Greenberg nor Rosenberg), reflects the waning power of these two Olympian critics. Ending rather abruptly, and with self-fulfilling prophecy, “Action/Abstraction” closes with “Marriage of Reason and Squalor” (1959), a completely flat and uninterestingly decorous canvas — an affront to Greenberg — by Frank Stella, and Allan Kaprow’s “Words” (1962), which is re-created at the Jewish Museum by contemporary artist Martha Rosler. Kaprow was the king of the “Happening,” in which the work — an Existential environment/arena for both artist and audience — demands participation. Its importance — as with “Action/Abstraction” — is not in the finished object but, rather, in the act.

Until September 21 (1109 Fifth Ave. at 92nd Street, 212-423-3200).