Aarhus or Hamburg?

Swimming is easier in Aarhus. Bellevue, Den Permanente and Moesgaard Strand are all within cycling distance of the centre, with fine sand and calm, shallow water, and there is a sea bath in the harbour too. The catch is the cold Kattegat, which limits the swimming season to a few weeks in summer.

Hamburg's sand along the Elbe at Oevelgoenne is for watching ships, not for swimming, because of the currents and the wash from passing ships. A proper swim means an hour's trip to the Baltic at Travemuende, where the water is hardly any warmer, or a lake on the city edge on a hot afternoon.

The two cities eat about equally well, but in different ways. Aarhus is at its best at the top end, with New Nordic tasting menus built on Jutland produce and fish from the bay, and rye sandwiches and cardamom pastries for everyday eating. It has few mid-range places and no real cheap end.

Hamburg is best at port food: fish rolls on the piers, Labskaus, eel soup and the early Sunday fish market in Altona. Portuguese and Turkish cooking near the harbour adds variety. Both are expensive, but Hamburg has more choice for a casual meal.

Here the cities are evenly matched but very different. Aarhus has three outstanding museums: ARoS with its rainbow walkway, the open-air Den Gamle By and Moesgaard with the Grauballe bog body. Around them is a small old core of Latin Quarter lanes and the long Gothic cathedral.

In Hamburg, the city itself is the main sight. There are the brick warehouses of the UNESCO-listed Speicherstadt, the ship-shaped Chilehaus, the Rathaus and the ruined spire of St Nikolai, and the Kunsthalle's Caspar David Friedrich paintings make a good indoor afternoon. Aarhus rewards museum-goers, while Hamburg rewards those who like to explore on foot.

Hamburg is the place for a night out. The Reeperbahn in St Pauli is famous across Germany, and bars have no fixed closing time. Each district has its own crowd, from the pavement bars of the Schanzenviertel to the smarter places by the Alster.

Aarhus fills up on Fridays and Saturdays, when students crowd the riverside bars on Åboulevarden and the cellar bars of the Latin Quarter. The scene is small, though, and midweek is quiet. It suits a drink after dinner rather than a weekend planned around going out.

Both cities sit in gentle, flat country, but Aarhus has the woods and Hamburg has the water. In Aarhus the beech forest runs right down to the bay, with tame deer to feed in Marselisborg, and the heathery hills of Mols Bjerge and the Silkeborg lakes are within an hour.

In Hamburg, being outdoors means paddling or sailing on the Alster, walking the Elbe path to the wooded slopes of Blankenese and cycling through the orchards of the Altes Land in spring blossom. Lueneburg Heath is an hour to the south.

Hamburg is the better base for day trips. Luebeck, Lueneburg, Bremen, Schwerin and Wismar are historic brick or half-timbered towns within about an hour by train. Luebeck, with its Holstentor gate and merchant houses, is worth a day on its own.

From Aarhus the trips are pleasant rather than outstanding. You can see the Tollund Man at Silkeborg, the runestones at Jelling, the cobbled old town of Ebeltoft and the Lego House in Billund. Odense and Ribe are a longer journey.

Both cities are easy with children, but the big attractions are in different places. Hamburg has them in town: the model railway at Miniatur Wunderland, Tierpark Hagenbeck with its tropical aquarium, and the harbour ferries and old Elbe tunnel. Most of these work on a rainy day.

Aarhus itself offers gentler things: Den Gamle By's old shops, the small Tivoli Friheden, deer to feed by hand and shallow bay beaches in summer. Its big days out, Legoland and the country's largest amusement park, need a car or a long bus ride.

Aarhus is a city you cross by bike. The centre is small and flat, with the station, ARoS, Den Gamle By and the harbour front a short walk apart, and wide separated lanes take you everywhere else. Buses run out to Moesgaard and the southern woods, and the light rail follows the coast towards Djursland.

Hamburg covers far more ground, so trains do the work there. The U-Bahn and S-Bahn reach every district, the harbour ferries double as a way to see the port from the water, and the airport has its own station. Wind and rain make cycling less pleasant, but in neither city will you miss a car.

Hamburg is well ahead for shopping. It covers every level from luxury to the high street to street markets, and Aarhus covers only a narrow band in the middle. In Aarhus most shopping happens on the single pedestrian street between the station and the river, which is lined mostly with Scandinavian chains. The city is at its best for Danish design, with small independent shops selling vintage, homeware, textiles and clean-lined clothing. There is almost no luxury and no market to browse.

Hamburg simply has more. The Alsterhaus on the Jungfernstieg sets the upmarket tone, Moenckebergstrasse and Spitalerstrasse cover the chains, and Ottensen and the Schanzenviertel are good for a slower look round smaller local shops. The long covered Isemarkt under the elevated railway is the kind of market browse Aarhus cannot offer. Maritime goods and tea or coffee from the old trading houses make more distinctive things to take home than anything on Aarhus's main street.

Neither city is cheap, but Aarhus is harder on the wallet. Meals, beer, coffee, taxis and museum entry all cost high Nordic prices. Bakeries, street-food halls, supermarket picnics and a bike are the ways to save.

Hamburg is expensive for Germany but easier day to day. One day ticket covers trains, buses and ferries, fish rolls and the casual places in Altona keep meals reasonable, and the Elbphilharmonie plaza and the Speicherstadt are free.

Performing arts are Hamburg's biggest advantage. The Elbphilharmonie and the Laeiszhalle give it two major concert halls, and the State Opera and the Hamburg Ballet are known worldwide. For lighter evenings there are long-running musicals and the St Pauli rock clubs where the Beatles started out.

Aarhus has a solid programme centred on Musikhuset, home to its symphony orchestra and the Danish National Opera, plus indie and jazz venues in the old railway yards. Its summer jazz festival and the late-summer Festuge arts week are when it is busiest. At other times there is less to choose from.

Aarhus bathes outdoors and Hamburg bathes indoors. In Aarhus the custom is Nordic: a round in a wood-fired sauna by the harbour or at Den Permanente, then a cold plunge into the bay, and visitors can join in all year.

Hamburg follows the German habit of long winter afternoons in warm bath complexes, from the art nouveau Holthusenbad in Eppendorf to larger sauna landscapes. For slower hours there are boat rides on the Alster and the Japanese garden in Planten un Blomen. Neither has thermal springs, and beyond the saunas both rely on hotel spas.