Andrea Palladio: His Life and Legacy, Royal Academy of Arts, London<br/> Le Corbusier: the Art of Architecture, Barbican Art Gallery, London

Even the venues underline how Palladio's starting point was the classical past, Corbusier's the future
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I hesitate to crack old jokes about exhibitions and London buses, but having major shows of Le Corbusier and Palladio come along at the same time does seem a touch de trop. If you have good arches and a stout pair of walking shoes, though, the pairing does make for comparisons.

The first to spring to mind is that both shows are being held in buildings based broadly on the ideas of the architects inside them. The Royal Academy's gallery block, home to Andrea Palladio: His Life and Legacy, was the brainchild of that great English Palladian, Richard Boyle, third Earl of Burlington. The concrete piloti of the Barbican Centre – the venue for Le Corbusier: the Art of Architecture – mark out its architects, Chamberlin, Powell and Bon (CPB), as equally fervent Corbusians.

The history of the two buildings also suggests something of the fate of the architects inside them. Burlington House is a mess. Palladio's reputation having nosedived in the mid-19th century, the Palladian details were stripped out of Boyle's one-time London home and replaced with the present Victorian ones. By contrast, the Barbican complex, once voted the ugliest building in London, was Grade II listed in 2001 for its "cohesiveness". All architects who did not study at the Prince of Wales's Institute of Architecture nurse dreams of living in it. Contemporary English Palladians are thin on the ground and build houses for Michael Heseltine. English Corbusians are beyond number and design for the readers of Wallpaper*.

Why should this be? The curating of the two shows gives some clue. The RA's Palladio-fest – the Paduan was born 500 years ago last year – is detailed and historicist: not unlike the architect himself, whose genius lay in grafting Greek and Roman motifs on to the villas of the Venetian rich. The result is that the academy's exhibition feels oddly Palladian, as though San Giorgio Maggiore had been rechristened San Andrea Palladio. Ignoring the reversal of its subject's fortunes that is Burlington House, the academy exposes his relics – a study of the Baths of Agrippa, fragments from the Quattro Libri – and asks merely that we worship them. It is a curatorial orthodoxy that does Palladio, an unorthodox thinker, no favours at all.

By contrast, the Barbican's show starts from the potentially subversive position that we should see Charles-Edouard Jeanneret, aka Le Corbusier, less as an architect than as a plasticien – a broad French term for anyone who makes things, whether they are watercolours or cathedrals. Corb feels at home among CPB's exposed concrete columns, which gives him an advantage over Palladio at Burlington House. But seeing his work in a novel way also suits a man in love with the new.

Among the many things that had changed between Palladio's birth in 1508 and Corbusier's in 1887 was the idea of what an architect was. The Italian was a master craftsman, apprenticed to a stone-cutter at 13; his Swiss counterpart went to art school. As a result, Palladio thought inside the box, even if that box might be round and pedimented. Corbusier found boxes annoying, unless they generated other boxes fractally or were bent out of shape. Palladio's starting point was the past, Corbusier's the future. His buildings were meant to look as no building ever had; his referents, accordingly, were artists rather than architects.

And so the lower floor of the Barbican's show is given over not to Le Corbusier's chapels and tower blocks but to his artworks. Truth to tell, these are not very good. Cubist or Tubist in style, Corb's paintings derive, sloppily, from his friends, Picasso and Léger. The sculptures are better, although this is because they were made by someone else: Joseph Savina, an actual sculptor. The day when an architect could, if called upon, carve his own stone was long gone by the 1930s. The day when artists had to be masters of their materials would soon follow.

It is a short walk from Corbusier's wood Sculpture No 7, made by Savina, to the miniature wooden Notre Dame du Haut by R Bleuse, maquettiste. The relationship between the artist's hand and his model and that model and the finished building has changed utterly from Palladio's day. Le Corbusier, godfather of the council estate, may have been unfairly lumbered by history with the phrase "a machine for living in", but his buildings are habitable sculptures. Whether that is a good thing, I should ask someone who lives in one.

Barbican Art Gallery, London EC2 (020-7638 4141) to 24 May; Royal Academy, London W1 (020-7300 8000) to 13 Apr