Copenhagen or Amsterdam?

Neither city is a beach destination, but Copenhagen makes swimming part of everyday life in a way Amsterdam does not. Its clean harbour has wooden bathing spots at Islands Brygge, Amager Strandpark is a few metro stops out, and Bellevue is a classic Øresund beach.

Amsterdam's nearest sand is at Zandvoort and Bloemendaal, half an hour away by train. Wind and the cold North Sea mean most visitors walk the beach rather than swim. In town, the IJburg beaches and the Sloterplas are only for hot weekends.

Copenhagen is the better place to eat. Its Nordic fine dining, built on foraging and local produce, brings travellers in on its own. Everyday food is good too, from smørrebrød lunches and cardamom buns to the Torvehallerne market halls and the natural wine bars of Vesterbro and Nørrebro.

Amsterdam's strengths are different: Indonesian rijsttafel, Surinamese roti, herring from street stalls, and the brown cafés and jenever tasting rooms where the early-evening borrel is the real pleasure. For dinner, go to De Pijp, the Jordaan or Oost rather than eating around Damrak.

Amsterdam has the greater collections. The Rijksmuseum, the Van Gogh Museum and the Stedelijk stand together on the Museumplein, and with the Anne Frank House they are of world rank. The UNESCO-listed canal ring is a sight in its own right.

Copenhagen's heritage is royal and maritime rather than artistic: the crown jewels at Rosenborg, the guard at Amalienborg, Christiansborg and the gabled houses of Nyhavn. The National Museum, SMK and the Glyptotek are good but not a reason to travel on their own. The modern design and architecture along the harbour add a layer of their own.

Amsterdam offers the better night out, especially for electronic music. Several clubs hold all-night licences in converted industrial buildings in Noord and on the edges of the centre, and the Amsterdam Dance Event takes over the city each October. The canal-side terraces of the Jordaan and De Pijp suit a slower evening.

In Copenhagen, going out centres on the converted butchers' halls of Kødbyen and the scruffier bars of Nørrebro, and the city centre has good cocktail bars. Weekends run late, but weeknights are quiet and the clubs are decent rather than a reason to come.

Both cities sit in flat country and offer gentle green escapes rather than wild scenery. Amsterdam's countryside is farmland: a ferry across the IJ leads into the polders, dykes and windmills of Waterland, and there is the Amsterdamse Bos and the bison in the Kennemerland dunes. Copenhagen has more forest and coast, with deer among old oaks in Dyrehaven, the Øresund cycle road to Helsingør and kayaking in the harbour in summer.

Amsterdam is the better base for day trips, because so many Dutch towns are close by on frequent trains. Haarlem, Leiden, Delft, Utrecht, The Hague and Rotterdam each offer a different city. Zaanse Schans, Volendam, Kinderdijk and, in spring, the Keukenhof add windmills and tulips.

Copenhagen has fewer outings, but they are good ones: Kronborg at Helsingør, Frederiksborg, the Louisiana museum and the Viking ships at Roskilde. What only Copenhagen offers is Sweden, with Malmö and Lund a short train ride across the Øresund Bridge.

Copenhagen is the easier city with children. Tivoli's old wooden rides are right by the central station, and Den Blå Planet, the zoo and the Experimentarium cover rainy days. Buses, trains and cafés are set up for prams, and the calm streets put parents at ease.

Amsterdam is welcoming too, with Artis, NEMO and the playgrounds of the Vondelpark. But fast bikes, unfenced canals and steep canal-house stairs mean small children need watching all the time.

Both are compact and flat, best seen on foot or by bike, and a car only gets in the way. The public transport is different. Amsterdam relies on trams through the canal ring and free ferries to Noord, while Copenhagen has a driverless metro that runs around the clock to the airport, plus yellow harbour buses. Copenhagen's wide, separated bike lanes may also feel more orderly to first-time riders than Amsterdam's busy ones.

The two are evenly matched but sell different things. Amsterdam is better for browsing small independent shops and markets, from the boutiques and vintage stores of the Nine Streets to the Albert Cuyp, Waterlooplein and the floating Bloemenmarkt. Copenhagen is the place for Scandinavian design, with furniture, lighting and Royal Copenhagen porcelain around Strøget and the old department stores Illum and Magasin du Nord, though it has few markets.

Both are among the most expensive cities in Europe, and neither suits a tight budget. In Amsterdam the biggest cost is the room: canal-ring hotels are very expensive and the tourist tax is high, so staying in Haarlem or Utrecht helps. In Copenhagen it is eating and drinking that cost the most, so visitors save with bakery breakfasts, supermarket picnics by the lakes and free sights such as the harbour baths.

Amsterdam has the edge, mainly because of the Concertgebouw, one of the world's great concert halls, with concerts most days of the season. It also has the opera house on the Amstel, the Muziekgebouw and Bimhuis, and the long-standing rock stages of Paradiso and the Melkweg.

Copenhagen has the Royal Danish Ballet and its Bournonville tradition, the harbourfront Opera House and DR Koncerthuset. Its long jazz tradition is at its liveliest during the July jazz festival. In both cities most theatre is in the local language, so visitors are better off with music and dance.

Copenhagen is the more restful city and has a bathing ritual of its own: wood-fired saunas floating in the harbour and on the beaches, followed by a cold plunge, all through the winter. Its calm streets and lakes make slow days easy.

Amsterdam has large day spas on its outskirts, mixed and nude in the Northern European way. Its centre is busy with visitors and bikes for most of the year, so quiet moments come from early walks along the canals or an afternoon in the Vondelpark.