In the blistering summer of 2003, I bundled a puzzled family into the car and headed off through the Vosges Mountains, in eastern France, to look at a small church on a hill in a semi-industrial landscape. We arrived panting, heat-struck, ill- tempered. But not for long. We had entered the presence of greatness. This was the pilgrimage chapel of Notre Dame du Haut, better known as Ronchamp, after the nearest village. It is the best-known work of one of the most celebrated and reviled architects of the 20th century, Le Corbusier. Built in the mid-1950s, it marked a decisive break from his machine aesthetic of boxes on stilts.

Ronchamp was weird, primitive, hand-crafted, powerful: the first postmodern building, and the best. Critics have argued about it loudly and continuously from the moment it was completed. It receives many more architectural pilgrims than religious ones. Then again, you come across a surprising number of people for whom Corb is God. And at least as many for whom, because of his provocative and influential early city plans full of skyscrapers, he is the very devil.

Corb, with his endless manifesto pronouncements and aphorisms (“A house is a machine for living in”), wrote the book when it came to architectural arrogance. “I don’t care about your church, I didn’t ask you to do it,” he coolly replied to Father Couturier, the artist-priest who hired him at Ronchamp. “And if I do it, I’ll do it my way. It interests me because it’s a plastic work. It’s difficult.” Corb’s prickly attitude did not dismay Couturier — he recommended his architect for the scarcely less celebrated later monastery of La Tourette, then died. It’s true what they say: great architecture happens only with great patrons. And Ronchamp is without question great. You know that the moment you see it, walk round it, into it. It is a small building on an extraordinarily epic scale. It is condensed genius.

This, of course, presents a bit of a problem for architecture exhibitions. An ambitious exhibition on Le Corbusier is about to open at the Barbican, in London, while a wonderfully old-fashioned show on the Renaissance master architect Andrea Palladio is running at the Royal Academy. As with Corb, with Palladio you really have to experience the real buildings. No photo, model, drawing or computer fly-through can truly communicate the impact of Ronchamp, or of the heart-juddering way you suddenly catch a glimpse of Palladio’s Villa Capra commanding its hill outside Vicenza. Or, for that matter, the moment you first walk into his extraordinary Teatro Olimpico, in Vicenza itself. There, too, you know instantly that genius has been at work. He was reinventing the ancient form of the amphitheatre for the modern world. As Corb was later to do, he also reinvented the form of the church — you see them dotted all over Venice.

Both exhibitions are big public ventures for what is the 175th anniversary year of the Royal Institute of British Architects (Riba), the 501st of Palladio, and the, er, 122nd of Corb. Riba invested heavily to bring the Corbusier show to Britain — first to Liverpool, now to the Barbican — and simultaneously supplied the RA from its collection of Palladio drawings, the most complete in the world. It’s been a while since the capital has had two such big-hitting architecture shows simultaneously in mainstream galleries.

And they are anything but lazy crowd-pleasers. When I saw the Le Corbusier show in Liverpool, in the Lutyens-designed crypt of the Metropolitan Cathedral, it seemed slightly confused, assumed too much prior knowledge. In the Corb-influenced surroundings of the Barbican, it may feel more at home. Similarly, with Palladio at the Royal Academy, there seems to be an assumption that visitors will be of a scholarly disposition, prepared to concentrate rather than flit. The combined message, however, is clear enough: remarkable individuals working in remarkable times produce remarkable buildings. Both Palladio and Corb were surrounded by talented contemporaries, but they made sure they rose to the top and stayed there.

The differences? Fewer than you might think. Both men, nearly four centuries apart, had a huge impact on the design of churches, houses, whole city districts. Both claimed to draw their inspiration from the ancient world and its mathematical proportioning systems. Both were associated with particularly fruitful periods in fine art. Both wrote wildly influential books to disseminate their ideas and beliefs. Both broke the rules to produce individual masterpieces that are sometimes eccentric to the point of wilfulness.

The real difference comes with their followers. Arguably, the later Palladian architects, particularly by the late 18th century in Britain and America, outclassed the master with their refined, progressive classicism. An English country house such as Holkham Hall, in Norfolk, is more Palladian than Palladio. The disciples of Corb, however, have so far mostly fallen far short. Corb did not wreck our cities in the post-war years — but those besotted with his early theories did, with chilling zeal. It’s like blaming Marx for Stalin. That was not the idea, at all, and Corb’s later town-planning exercises prove he had changed his views utterly. He was always several steps ahead of his baffled adherents, right up to his death in 1965.

The pilgrimage chapel at Ronchamp remains as a kind of architectural sphinx. It has been analysed to bits, but we are no closer to really understanding the impulse behind it. In the end, it’s best not to try to understand. Just think of it as architecture that, like Palladio’s, is very close indeed to some kind of absolute truth.

Le Corbusier: The Art of Architecture, Barbican, EC2, from Thursday until May 24; Andrea Palladio: His Life and Legacy, Royal Academy, W1, until April 13

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