The first things the visitor sees are the treasure chests. Strong and functional yet ornately decorated, the ranks of chests against the wall are a silent reminder of an eloquent truth. The building of a global empire is principally about the commodity the original owners of these imposing boxes hoped to fill them with: money.

In Amsterdam, the city museum has just opened a fascinating new exhibition. They call it simply De Gouden Eeuw (The Golden Age). The age in question is the one that followed the 16th-century Dutch revolt against Spanish rule. The Netherlands became a world power within the space of not much more than a generation. It was also an age of Dutch enlightenment, the age of Rembrandt, Spinoza, Grotius and Huygens. In those years, Amsterdam was the capital of the world.

That era has long been called the Dutch golden age by historians. Yet an exhibition like this raises wider questions for all postcolonial European nations, including Britain. Can any age of empire, which this certainly was for the Netherlands, be described in something like an exhibition as a golden age? And, how should modern European nations like Britain and the Netherlands present their imperial past to the public? These are not just academic questions. Amsterdam's answer is full of lessons.

The Amsterdam team are not blind to the ironies, or even the hypocrisies, that can sometimes be found behind continuing too confidently to a golden age. As good 21st-century exhibition curators must, they shine their light, a little diffidently at times, on the sordid as well as the splendid aspects of Dutch power. They also deftly point out lots of cultural and political connections and contrasts between Rembrandt's Amsterdam and that of Geert Wilders today.

Nevertheless, you cannot miss the reality that the Amsterdam show exhibits a palpable, continuing pride in the Dutch nation their ancestors created four centuries ago (Amsterdam will also celebrate the 400th anniversary of its canal system in 2013, by the way). And even today the Dutch seem to have strikingly few hangups about describing their country's defining years as golden.

On one level, it isn't at all hard to see why. In a few short years at the end of the 16th and the start of the 17th century, the Dutch republic made itself the hub of the world. State of the art shipping, weapons and science enabled them to capture and dominate the lucrative spice trade with the East Indies. Back in the Netherlands, the wealth and freedom fuelled by this trade brought a glittering age of writing, painting and technological invention. Their freedom of press and religion was a magnet to the rest of Europe. Its primary monument remains Amsterdam itself, so it is easy to feel the connection to this day.

In his modern classic, Vermeer's Hat, Timothy Brook says simply that 17th-century Netherlands raised the curtain on the global world – which is our world. The Dutch bought and sold wherever they could find anything to trade. They wrote the fundamentals of international law to suit their needs. They mapped the globe and the heavens. Their way of life became multicultural. When Vermeer painted a geographer in 1669, he dressed him in a Japanese kimono and gave him a globe depicting the Indian Ocean.

The Amsterdam exhibition tracks all these aspects of globalisation's first wave. The Dutch established colonies in modern-day Brazil, South Africa, Sri Lanka and Java – and on Manhattan, too. Theirs was a connected world. In a 1656 picture of the centre of Amsterdam, Ottoman merchants are shown negotiating a deal just round the corner from where the picture itself now hangs. A Dutch translation of the Qur'an was printed there in 1696.

But this was a time of slavery and war too. Slavery was illegal in the Netherlands, but Dutch ships carried and sold slaves in Africa and Surinam, and Dutch fortunes waxed rich from the profits of the trade. The Dutch were renowned in China for their violence, and their arms industry – still the sixth-largest in the world today – was formidable. By modern standards, Dutch justice was anything but enlightened. Two ghoulish Rembrandt drawings of the public strangulation of a female murderer depict one of the many dark sides of the golden age.

As a British visitor one constantly notices parallels and contrasts. England, in particular, had much in common with the 17th-century Netherlands. Both were northern Protestant republics (briefly in England's case) with strong navies, ambitious commercial elites and a degree of freedom of speech unusual for the time. There is much in the Amsterdam show that resonates across the North Sea.

Eventually, however, Britain became richer and more powerful, while the Netherlands dwindled in influence. London became the global city that Amsterdam had once been. The British empire was larger and lasted longer. The English language created a network of soft power that nowadays extends even into every corner of Anglophone Amsterdam itself. Yet we would never call ours a golden age. It is impossible to imagine an exhibition on 18th- or 19th-century London that would make such a claim. The only golden age this country acknowledges with any confidence is the 2012 Olympic Games.

Perhaps the explanation is only that Dutch prowess began to dwindle so long ago compared with Britain's more recent decline. Certainly, modern-day Netherlands is extremely conscious that it is now a small country, dependent on European alliances in a way that is manifestly not mirrored in increasingly Eurosceptic Britain. Perhaps a small country feels permitted to dwell on a distant golden age in a way that a bigger one does not.

Or perhaps the explanation is simply that the British have not yet learned how to agree an account of the age of British global power and wealth. It would be fascinating to see a credible attempt to contain such a subject within an exhibition similar to the one the Dutch have just mounted in Amsterdam. It would be great to try.

The subject may seem too big, too raw and perhaps still too politicised – until one visits the German Historical Museum in Berlin and realises that tougher assignments have been successfully carried out. A satisfactory alternative modern narrative of British power remains to be written. Perhaps this absence of a settled history helps explain why Britain has such difficulties with its relationship with the EU. Or perhaps – a nice thought with which to end the year – our golden age does not lie behind us. Perhaps, echoing Milton, our own golden poet, the world is all before us.