Anyone who’s ever taken an art history course knows the drill: put two artworks side by side, and figure out where they intersect and diverge. The exercise involves IDing those objects, stating who made them and why, and accounting for formal innovations across time and cultural differences. Essentially, the discipline is predicated upon a gussied-up game of compare-and-contrast.

“Costume Art,” the Metropolitan Museum of Art ’s big Costume Institute show for the spring season, attempts to continue the tradition. People will flock to this blockbuster to see rarified dresses in sleekly designed galleries, as they always do. But this time the stars of the show also include artworks from the Met’s collection placed next to the fashion on display.…