The triumph and tragedy of the rival expeditions, their differing ethos and the fearsome conditions of the Antarctic, are the stuff of a drama that has never lost its power. The Scott centenary next year will resurrect the debate about how he should be remembered; this year the Norwegians have allowed themselves a modest celebration of Amundsen's success. It culminates in Oslo on "South Pole Day", December 14, when King Harald unveils a monument to the five men who got there first.
I visited the places in Amundsen's homeland that were key to his life, and unwittingly found myself blazing an "Amundsen trail" through some of the most attractive bits of the south of the country. Hvaler, for instance, just south of Oslo, is where his grandparents lived and the keel of the family shipping business was laid. It's a fractured band of small islands at the entrance to the Oslofjord, strung together with bridges and a single main road. Supposedly it is the sunniest corner of the country.
Hvaler is a coastline of granite the colour of basking seals, rubbed flat as old soap by the Ice Age. Bright timber buildings crowd its quaysides and speckle its fields. The seaside holiday homes have the unmistakable sheen of prosperity. In the Amundsens' day, Hvaler was a harsh outpost of tough seamen and fisher folk. The family home, on the island of Kirkøy, is now the Sandbrekke guesthouse.
As their shipping business grew, the Amundsens moved to the mainland. Roald's father, Jens, built Tomte, a pantiled cottage of white timber, beside the River Glomma, near Sarpsborg. There, in 1872, Roald was born. In summer, Tomte is opened as a museum.
Nearby, smarter than when Amundsen was a boy but not much changed otherwise, is the old garrison town of Fredrikstad, founded in 1567. Now, snugly contained by the river on one side and a moat and earthworks on the other, it's a photogenic concentrate of old Scandinavia, a fortified country town of handsome buildings of rosy brick and classic, pastel-painted weather board. Thanks to a succession of fires, the architecture is mostly from the 18th century. The church, built in 1779, is the sixth on the same site.
Upriver from Fredrikstad, Tomte was a substantial residence for its time, with six ground-floor rooms and servants' accommodation in the loft. Jens's fortune had come from supplying the British Army in the Crimean War; a cannonball is displayed in the drawing room.
There are other souvenirs of a seafarer: a parasol, pram and furniture from China – Jens and his wife Hanna voyaged there on their honeymoon – and a mug from Exmouth. Hanna wanted Roald to be a doctor but, not for the last time in his life, he had other ambitions.
Uranienborg, an ample grey and white chalet on the banks of the Oslofjord, is also a museum. This was Roald Amundsen's home for 20 years before his death in 1928 in an air crash, in the Arctic, searching for a missing Italian explorer. The house was built in 1898 by a Swiss, which accounts for the wide-splayed gables and ornate straps of fretwork. Visitors are shown Amundsen's upstairs study and mementoes from his polar travels – a sledge, map, compass and flag from the Antarctic, a medicine chest, sun glasses and ski wax.
In the living room is a monochrome photograph of the English explorer Sir John Franklin, who in 1845 led an expedition to chart the Northwest Passage. He and his 126 companions disappeared without trace or explanation. It was a story that hijacked the imagination of the teenage Amundsen, and supplied the first set of bearings for the course his life would take.
There is a quote from Franklin, beneath the picture, about the centuries-old grail of establishing a northern route between the Atlantic and the Pacific. "It might be done," he said. "And England should do it." England didn't; Amundsen did.
It took him three years, from 1903 to 1906, almost two of which he spent with the Netsilik, an Inuit people in what is now the Canadian territory of Nunavut. An exhibition in Oslo's Museum of Cultural History, entitled Arctic Experts, contains many of the 1,200 items that Amundsen himself collected. It runs until June and illustrates some of the lessons he learnt from the Inuits. It was they who persuaded him of the value of dogs for hauling sledges. Norwegians at that time tended to use reindeer. Scott would rely on ponies and people.
Dogs were efficient; they were also edible. In one day, en route to the Pole, Amundsen's dog teams covered more than 10 miles and ascended 5,000ft. The previous day, 24 huskies were slaughtered. In Amundsen's words, they were "given the best reward: death". In a letter to Amundsen's brother, discussing arrangements for Roald's 1912 lecture tour, the secretary of the Royal Geographical Society wrote: "I think also it may be as well to omit all mention of what he calls the 'butchery' of the dogs." Amundsen left his base camp on October 20 1911 with 52 dogs. On his return, three months later, there were 11.
He abandoned heavy European woollen clothing for Inuit parkas, made from short-haired caribou skin. Tone Wang, a teacher at the museum, told me how the macho explorers had cut off the tassels round the parkas' hems because they thought they looked effeminate – and then sewn them back on again when they discovered they had the practical purpose of helping to keep their hands dry.
One of the other advantages the Norwegians had was their innate proficiency on skis. Scott recognised the value of skiing, ironically from his visits to Norway. On three occasions he stayed at the Fefor Hotel, then one of the most fashionable resorts in Scandinavia. Some three hours by train north of Oslo, the original 120-year-old building still stands. Constructed like a massive log cabin from hefty trunks of pine, it has been much extended over the years.
Scott chose the slopes at Fefor to test a tracked motor sledge, two of which he took to the Antarctic. There they were not a success: at Fefor they were. Ragnar Jacobsen, who was the hotel's manager for 20 years, tells how a hundred locals piled on to sledges and were mightily impressed when the tractor successfully dragged them uphill from the shores of the lake.
During the trials, an axle broke and needed to be taken to the blacksmith in Vinstra, eight miles down the mountain. A wealthy young Norwegian adventurer, Trygve Gran, made the return journey on skis with the axle on his back. Scott signed him up as the expedition's ski instructor.
I met Gran's 67-year-old son, Herman, aboard the Fram, the ship that took Amundsen to the Antarctic, in its eponymous museum at Bygdøy, just outside Oslo. It is there that the new monument to the polar party has been erected. A tubby little three-masted schooner, it hardly looks like one of the world's legendary boats. Designed to withstand the pressure of pack ice with hull sheathed in steel-hard greenheart wood, Fram had already made two Arctic voyages before Amundsen sailed south.
The Norwegians' professionalism in the Antarctic is illustrated in a new exhibition at the Fram Museum. They shaved packing cases with an axe, planed their skis and rebuilt their sledges to reduce weight – that of the sledges by more than half. They packed 42,000 biscuits by hand to save space.
Fram was built for Fridtjof Nansen, explorer, scientist, athlete, diplomat, winner of the Nobel Peace Prize and revered in Norway. Amundsen had Nansen's approval to take Fram to the Arctic, the sea for which it was designed, to attempt to reach the North Pole. But while Amundsen was still planning his expedition, two Americans, Frederick Cook and Robert Peary, separately claimed the North Pole for themselves.
Cook's claim now is discounted and Peary's remains debatable, but in 1909 they were enough for Amundsen secretly to change his mind and prepare to head south. Not until Fram reached Madeira in September 1910 did he even tell his crew where they were really going.
The news was awaiting Scott in a terse telegram when he arrived in Melbourne in October: "Beg leave to inform you Fram proceeding Antarctic. Amundsen." Trygve Gran was now in the invidious position of competing with his compatriots. According to his son, Trygve would never have accompanied Scott had he known Amundsen's true intention. "But he always talked about Scott favourably," Herman told me. "He was very loyal. He never accused Scott of anything."
In all the controversy that swirls around the two expeditions, one of the most moving and perceptive epitaphs for Scott came from Trygve Gran. He was in the search party that found the frozen bodies of the British explorers. He wrote: "I almost envied Captain Scott as he lay on the field of honour. He had achieved something great for his country, for his family and indeed morally for the whole of mankind."
Gran made a cross of his own skis to mark the makeshift tomb of piled snow. Scott's skis he brought home and donated to the Ski Museum at the Holmenkollen ski jump near Oslo. For a Norwegian, the act was a little like recovering the helmet of a medieval knight from the battlefield where he had fallen. In the end, honour is all.
SAS, British Airways and Norwegian fly to Oslo from Heathrow, Gatwick, Manchester and Edinburgh. Norwegian one-way fare from £36 inc taxes (020 8099 7254; norwegian.com). Norwegian railways, NSB (nsb.no), run to all of the destinations visited by Peter Hughes.