A scant half-hour out of Grand Central takes you to the Bruce Museum in Greenwich, Conn., and New Yorkers are lucky to be so close to it.

“Painterly Controversy: William Merritt Chase and Robert Henri” is the Bruce’s major winter exhibition. Thirty-four paintings borrowed from across the country illustrate the stylistic parallels and crucial differences between two of the most adored and influential American painters at the turn of the 20th century.

It is a lively, illuminating tour through a tempestuous relationship that became a watershed in the course of American art. One fascinating feature is the selection of the men’s classroom demonstration pieces, blueprints to their teaching styles, plus classroom work from their students: Stuart Davis, Rockwell Kent, Georgia O’Keeffe, and Edward Hopper. Chase’s virtuosic “Young Girl” (c.1900) is a breathtaking evocation of a living presence completed in about an hour while students watched.

On view are some of the pair’s loveliest and most characteristic works, including Chase’s “Carmencita” (1890) and Henri’s “La Madrileñita” (1910). Henri’s magnificent 1904 portrait of John Sloan (who often substituted for him in class) reincarnates Velazquez’s “Portrait of Pablo de Valladolid” (1632). Chase’s 1882 painting of his famous 10th Street studio interior conveys his cosmopolitan image.

In 1902, the eminent Chase (1849–1916) hired the younger, left-leaning Henri (1865–1929) to teach at the New York School of Art, founded in 1896 as the Chase School (now Parsons School of Design). It seemed an inspired choice. Both men were charismatic teachers and top-drawer portraitists. Both acquired the subdued palettes and lively brush work of Manet, Velázquez, and Frans Hals. Both took their easels outdoors to capture the American scene. These correspondences are amply represented.

But the two diverged over methodology: the role of technique, draughtsmanship, and subject matter. Chase, renowned for technical accomplishment, urged mastery as a critical component of artmaking. His emphasis paralleled that of the early 20th-century avant-garde, particularly the Russian Constructivists. But among students at the New York School, the fastidious Chase was rear guard. Henri, breezy about skills, was the favorite. He played the piper to youthful self-confidence: “Can’t we ever realize it is not for the old to judge the young — that it is the young who must judge the old.”

Chase, a connoisseur of European painting, was one of the first American painters to apply Impressionist techniques to local landscapes. Henri dismissed Impressionism as “the new academicism.” While Chase trusted technical means to elevate all subjects, he advocated ones with a certain inherent aesthetic appeal. Henri defended gritty, urban motifs.

Within five years, their differences strained compatibility beyond repair. In 1907, Chase left the school he had founded. New York newspapers blared the rift: “Wm. Chase Forced Out of New York Art School: Triumph for the ‘New Movement’ Led by Robert Henri.”

The catalog provides engaging anecdotal material. It is fun to know that “Brushwork Chase” could paint quickly enough to rent a fish for a still life, promising to return it in an hour. Nice to learn that “For his male students, Henri was defined by his masculinity.” (The childless Henri’s masculinity is defined, however, solely in terms of ball playing and roughhousing.) It is exciting to look in on what Henri termed “the big fight.”

Nevertheless, art belongs to the history of ideas; and ideas have real consequences. The exhibition’s didactic script, beautifully illustrated, stops short of drawing the conclusions implicit in the rivalry it documents.

The most obvious is that the earliest American modernists, like their European counterparts, were trained in traditional methods and problem solving. These were the bedrock that permitted artists to successfully break new pictorial ground. Henri’s advice to “get the principle of it, but not the mannerism” depends on just the kind of training he himself had. Minus that rigor, art slips into the sandbox.

Henri admired anarchist Emma Goldman and taught, for a time, in her Ferrar School. “Red Emma” sat for her portrait, declaring Henri “an anarchist in his conception of art and its relation to life.” His contest with Chase translated antinomian enthusiasms into an emancipatory pedagogy: “I do not want to see how skillful you are—I’m not interested in your skill,” he wrote in 1923. “What is life to you? … What are your deductions? What projections have you made? What excitement, what pleasure do you get out of it?” Henri insisted that the object of artmaking was “the attainment of a state of being” of which the art was but “a byproduct.”

Roads to the opium den of selfexpression are paved with such stirring stuff. But the museum neutralizes the history in its grasp by smiling on Henri’s “boldness and openness to new ideas.” Cultural memory shrinks to a cheer for the heady and the new.

Until April 29 (1 Museum Drive, Greenwich, Conn., 203-869-0376).