Coming of Age, Dulwich Picture Gallery London<br /> The American Scene, British Museum London

I would normally avoid singling out any work as the most important in a show, though there is no way of doing so with Josef Albers' Bent Back (A) and Dulwich Picture Gallery's Coming of Age: American Art 1850s to 1950s. Albers' abstract, of 1940, looks like an open door, and so it is. Step through it, and you're in the last room and decade of this silly exhibition – the moment when American art finally gets around to doing what the show's title has promised it will.

With Albers, a refugee from the Bauhaus, New York suddenly takes off as the epicentre of Western art, a place of hard edges and hard thinking. Walk through the decades and rooms before Bent Back (A), though, and you find yourself wondering what would have happened if German artists hadn't had to flee Hitler; whether America's art, like her rocket programme, doesn't owe Nazism a debt of gratitude.

This is not the view taken by Coming of Age, which sees the greatness of American art after 1940 as essentially home-grown. According to the show's catalogue, the art of the USA "evolved ... over the course of 100 years, from the provincial to the international"; an idea which, if you will excuse my French, is bollocks.

There is no linear progression in this show towards the sudden burst of genius embodied in Abstract Expressionism and catalogued by Clement Greenberg; rather the opposite, in fact. For all that the 1913 Armory show hit astonished New Yorkers with the European distortions of Cubism and Fauvism, American art for the most part remained doggedly parochial and backward-looking. To be sure, there are flashes of genius in the general dullness that marks the first five-sixths of this show; Whistler's Old Battersea Bridge of around 1860 and Man Ray's Ridgefield (1913) lodge in the mind as examples. But Man Ray had clearly been looking at Kandinsky rather than at Winslow Homer when he painted his picture, and both he and Whistler fled to Paris as soon as they could.

So why make American art out to be something that it wasn't? I can only assume that the curators of this sad little show wanted to flatter its lenders, the Addison Gallery in Massachusetts. If so, they have failed badly. Any attempt to sum up a century of national art-making in half a dozen cramped rooms and 70 necessarily small-scale pieces was bound to end up looking jejune, and Coming of Age does just that. Much of the most interesting American work pre-1940 was presumably either missing from the Addison's collection or simply too big to be shown. Thus, for example, there is nothing by Thomas Hart Benton here, although Benton's Regionalist murals are hugely important and one of his students was Jackson Pollock. Although the comparison is unfair, I couldn't help thinking of last year's magnificent Art in America show at the Bilbao Guggenheim, an exhibition whose vast numbers and spaces (and vastly intelligent curating) did its subject justice. Coming of Age moves on to the Peggy Guggenheim Collection in Venice after Dulwich. What the notoriously fussy Italians will make of it can only be imagined.

By contrast, the British Museum's The American Scene: Prints from Hopper to Pollock, uses twice as many works as the Dulwich show to look at a moment in US art that is half as long and involves a single medium. The American print really came into its own in the years around the Great War, its rapidity, expressionist contrasts and demotic prices chiming with the era's new fondness for the Common Man. Prints being self-effacing things, many of the works in this show are hardly known outside of the US. Yet The American Scene reveals print-making as a laboratory for home-grown experiment on a scale that can not fail to amaze.

"Realism" is an easy word to bandy about, as the Dulwich show proves. It was on paper rather than on canvas that American Realism really found its voice, though, with artists like George Bellows and Louis Lozowick evoking a world that was genuinely, if bleakly, modern. Lozowick's dark celebration of the city takes on the other big challenger for supremacy in American image-making: not Europe, but the cinema. And Bellows's lithographs of boxing bouts and executions may have their origins in Goya, but they lead, inexorably, to Andy Warhol's "Electric Chair" paintings of the 1960s. You can find out far more about American modernism in this focused show than from all the hyperbole of Dulwich, and save yourself £9 into the bargain.

'Coming of Age', Dulwich Picture Gallery, London SE21 (020-8693 5254) to 8 June; 'The American Scene', British Museum, London WC1 (020-7323 8000) to 7 Sept