Copenhagen or Hamburg?

In Copenhagen swimming is part of ordinary city life. The harbour is clean enough to jump into from the wooden baths at Islands Brygge, and the sandy lagoon beach at Amager Strandpark is a few metro stops from the centre.

Hamburg has sand along the Elbe at Oevelgönne and Blankenese, but currents and the wash from ships make it a place to watch freighters, not to swim. For a real sea swim you need a day out to the Baltic at Travemünde. Neither city is a beach destination, but only Copenhagen lets you swim between sights.

Copenhagen is the city to choose for eating. It helped redefine Nordic cooking, and some visitors come for its foraging-led fine dining alone. Day to day there is smørrebrød on rye, the Torvehallerne market halls and natural wine bars in Vesterbro and Nørrebro.

Hamburg eats well but more plainly, as a port city does: a herring or shrimp roll at the Landungsbrücken, Labskaus and eel soup, and Portuguese and Turkish cooking near the harbour. Both cities love a cinnamon pastry for breakfast. Copenhagen has the better food but charges more for it, while Hamburg's prices are high for Germany and still easier to manage.

Copenhagen has more classic sightseeing. Rosenborg with the crown jewels, Amalienborg's changing of the guard, Christiansborg over its medieval ruins and the gabled houses of Nyhavn make a royal centre that survived largely intact.

Hamburg's appeal is commercial and industrial: the UNESCO-listed Speicherstadt warehouses and the Chilehaus, the Elbphilharmonie plaza and the war-ruined spire of St Nikolai. Much of the old town was lost in the Second World War, so you explore it district by district along the water. The Kunsthalle's Caspar David Friedrich paintings are its museum highlight.

Hamburg is the place for a big night out. Along the Reeperbahn in St Pauli, bars have no fixed closing time, and a night of neon, cabaret, music clubs and dive bars can end at dawn by the harbour. The Schanzenviertel and the smarter bars around the Alster give it range.

Copenhagen's evenings are more refined and more expensive. There are cocktail bars in the centre and converted butchers' halls in Kødbyen, and in summer people drink by the canals at Nyhavn into the light nights. It is a good scene, but not one people travel for.

Both landscapes are flat, but Hamburg gives you a little more to do. You can sail or paddle on the Alster lakes, take a canoe up the northern canals, climb the steep wooded lanes at Blankenese and cycle the Altes Land orchards in spring blossom. Lüneburg Heath is about an hour away.

Copenhagen's outdoors is gentler. Deer roam among old oaks in Dyrehaven, the Øresund coast road makes a lovely ride to Helsingør, and you can kayak in the harbour. The chalk cliffs of Møns Klint, its most dramatic scenery, are a two-hour trip.

Both are excellent bases, and the choice comes down to what you want to see. From Copenhagen the outings are castles and art: Kronborg at Helsingør, Frederiksborg, the Louisiana museum on the coast and the Viking ships at Roskilde. Malmö and Lund are a short train ride across the bridge, so you can add a second country to the trip.

From Hamburg, trains reach the brick Gothic towns of the Hanseatic north. Lübeck is the first choice, followed by Lüneburg's leaning gables, Bremen's market square and Schwerin's castle on its lake.

Copenhagen is easier with children because the whole city works that way. Tivoli's old wooden rides are next to the central station, buses and trains take prams as a matter of course, and Experimentarium and the old Bakken fairground are a short train ride away.

Hamburg has fine single attractions. Miniatur Wunderland can fill a rainy afternoon, Tierpark Hagenbeck shows animals without bars, and a ferry plus the old Elbe tunnel makes a harbour adventure. It also has Heide Park and Hansa-Park within about an hour, the kind of big theme park Copenhagen does not have.

Both are among the easiest cities in Europe to get around without a car. The difference is how you travel. Copenhagen is a bicycle city, with separate lanes that have their own traffic lights, and the driverless metro runs all night to the airport.

Hamburg works better by public transport. The U-Bahn and S-Bahn reach every district, and the harbour ferries are on the same ticket, so a ride across the port is a cheap sightseeing trip. Its main station also connects to the whole of northern Germany.

The two are closely matched, but they sell different things. Copenhagen is for design hunters: furniture, lighting and ceramics shops around the centre, the Royal Copenhagen flagship on Amagertorv, and Scandinavian labels in the Latin Quarter.

Hamburg suits fashion shoppers better. It has luxury labels on Neuer Wall, covered arcades for wet days and the Alsterhaus on the water. It also has the markets Copenhagen lacks, the long Isemarkt under the elevated railway and the Sunday fish market.

Neither is cheap, but Hamburg costs clearly less. Hotels, restaurant meals and drinks in Copenhagen are expensive at every level, so visitors there rely on bakeries, supermarket picnics by the lakes and a rented bike.

Hamburg is pricey for Germany, especially during trade fairs and on summer weekends. Even so, fish rolls, the casual places in Altona and St Pauli, and a day ticket that covers the ferries make daily spending noticeably easier.

Hamburg has the stronger stage. The Elbphilharmonie is one of the great modern concert halls, and the Laeiszhalle, the State Opera and the Hamburg Ballet fill out the classical calendar. On top of that come Germany's biggest musical theatres, some reached by boat, and the St Pauli club circuit where the Beatles cut their teeth.

Copenhagen is more specialised. The Royal Danish Ballet keeps up the Bournonville tradition, DR Koncerthuset has superb acoustics, and the July jazz festival fills the squares and courtyards. Most theatre there is in Danish, so visitors usually choose music and dance.

Copenhagen is the more restful of the two. It is built around hot and cold bathing: wood-fired saunas float in the harbour, and locals plunge into the cold water through the winter. The quiet, orderly pace of the city and slow afternoons by the lakes add to the calm.

Hamburg shares the sauna habit but keeps it indoors, in the art nouveau Holthusenbad and large bath complexes where locals spend winter afternoons. A boat around the Alster or the Japanese garden in Planten un Blomen makes a pleasant break, but you would not choose the city for wellness.