The new Bilbao Guggenheim is the world's most exciting modern building. It outranks the Sydney Opera House and the Ronchamp Chapel. It outshines the Pompidou Centre and the Getty, Pei's Louvre Pyramid and Foster's Hongkong Bank. The building is designed, or rather sculpted, by the American Frank Gehry, and sits in a railway yard in northern Spain. It is the only work of art I know in which pure abstraction yields so vivid a sensation of beauty.

Bilbao is one of Europe's least appealing cities. The industrial port for the Basque country clings to a scruffy riverbank as if in the American rust-belt. The road from the airport snakes over the hill and down between bleak housing estates into the centre. Mist rolls in from the Atlantic. Suddenly from amid a mess of bridges, car parks and sidings rises a desert rose, glowing silver and gold. In form it might be a crumpled pile of fishtails, boats, bottles and packing cases. Yet the pile is translated by Gehry's artistry into an eruption of fantastic petals, each obeying a logic of its own, unshared with the world. For those who loathe the very idea of modernism in art, Bilbao is a stunning corrective.

Back in England, Wednesday saw the topping-out ceremony for the new Tate Gallery on London's Bankside, like Bilbao a heart transplant into a decayed city centre. Contrast was never more stark. The new Tate is intended to house the modern paintings and sculptures that cohabit with the "historical" British collection on Millbank, freeing each from the incubus of the other. It is being slotted inside the former Bankside power station, and will be invisible from outside. Seen from the City, London's most daring new museum will not jar, or shout or even glow. It will look as before, like a power station.

The Bankside Tate will be a thoroughly British sensation, introverted, straitjacketed into its context, a quart in a pint pot. Nobody would today allow a power station to be built beside the Thames. They would much rather an art gallery. But a power station they have, and so a power station it must remain. In Britain, new uses must find houseroom in the carcasses of old ones. Perhaps appropriately, the gallery has been designed by the Swiss architects, Herzog and de Meuron. There will be no laughs on Bankside, just hard work, efficiency, coolness and clean. This is, after all, a power station. Jokes are for Bilbao.

The critic Hugh Pearman this week publishes his magisterial Phaidon catalogue of the best 600 buildings of the last quarter of the 20th century. Few are in Britain, despite the role played by such architects as the Stirling-Foster-Rogers triumvirate in "postmodern" design. More astonishing still, not one of London's three most lavish new arrivals - the Tate, the Royal Opera House and the new British Museum Great Court - will be visible from the street. Though all cost roughly twice Bilbao's £65 million, they are models of self-effacement. Elsewhere, James Stirling's last work, Number One Poultry, is already merging into its surroundings opposite the Mansion House. As for the Parliament building next to Big Ben, it was revealed this week that £34 million was needed for special cladding, "to help it fit into its historic surroundings". Modern British architecture might have vanished to a nunnery.

This is understandable. The British public is still suffering concussion from the battering it took from Modernism during the 1960s and 1970s. As Pearman remarks, the later work of many British architects will be repairs to their earlier work. Most of the buildings now emerging from scaffolding in city centres across the country are re-claddings, as if ugliness could be hidden under pancake makeup. Architecture is the profession whose work imposes itself most forcefully on the public, yet which has no quality control or self-discipline. Erect an unusable or hideous building and you are more likely to win a prize than get struck off.

So how was Bilbao lucky? The city had guts and tried harder. Its civic leadership - a concept permitted in Spain but not in London - realised that dramatic public buildings sell cities. Multinational arts foundations are as potent inward investors as multinational car firms or microchip companies, indeed more so. Durham should have lobbied the Guggenheim Foundation, not the Japanese. Siemens and Fujitsu come and go. Museums are forever.

When asked, Why Bilbao? the Guggenheim's director, Thomas Krens, boasted that "a museum does not have to be at the centre of the universe. If art is significant, people will come to see it. They will make a pilgrimage." They will make that pilgrimage even if, as at Bilbao, the contents may not be worth much. There are works by Serra, Koons and Oldenburg but the chief exhibit is the museum itself. Visitors walk round the outside, then inside, then gaze up at the atrium with its labyrinth of gantries and funnels, then wander back out. They cannot take their eyes off the building. It changes its face with each passing cloud and each declension of the sun. The place inhales light. It needs no extra art.

What inspired Frank Gehry to produce the Bilbao shapes remains a mystery. According to the guide, it began as a flower doodle, with petals arranged round a central stalk, but was transformed variously into a boat, a fish, a snake and "my little mudpie" of polynomial equations. Gehry hates straight lines. He loves the humour of a curve. One of his buildings, in Prague, looks like a drunk leaning on a lamppost, another in Venice California is a huge pair of binoculars. In Bilbao he wanted a building that reproduced the plasticity of that original doodle. When his sweeping, wayward curves seemed impossible to engineer, he turned to a computer borrowed from French aerospace, to make each component robust, light and easy to manufacture. The exterior was covered in titanium leaf scales, applied by hand to create a silver-gold quilt, billowing and crinkling in the sun. The leaves reflect pure, warm light, not the cold mirror images of glass. The metal seems as natural as wood.

The Guggenheim story points a dozen morals. Bilbao has commissioned not just a museum by Gehry but an air terminal by Santiago Calatrava and subway stations by Norman Foster. With three bold commissions, the city has transformed its image as drastically as did Sydney with its opera house and Stuttgart with its art gallery. These structures are the pilgrimage churches of our age. They distribute their wealth as liberally as they distribute their aura. They are huge "people draws". Half a million visitors a year were predicted for the Bilbao Guggenheim, yet in its first six months, it took 700,000 (with no nonsense about free entry). It is already Spain's second tourist attraction after the Madrid Prado. British Airways reservations on its direct flight to Bilbao are up 20 per cent.

Half the buildings in Pearman's "600" are related to the arts and leisure. They include art galleries, opera houses, concert halls, libraries, sports stadiums, public spaces, parks. These are all venues of congregation and enjoyment, symbols of confidence in the humanities and in the future of cities. They are factories of pleasure. Almost all are exhilarating, works of style, inventiveness and colour. The contrast with the previous quarter century could not be more forceful. A similar book on my shelf (Twentieth-century Architecture,