Copenhagen or Reykjavik?

Neither city is a beach destination, but Copenhagen at least gives you a real summer swim. You can jump straight off the quay at the Islands Brygge harbour baths, Amager Strandpark's long sandy shore and lagoon are a few metro stops out, and Bellevue to the north has its whitewashed lifeguard towers.

In Reykjavik the sea is North Atlantic cold even in July, and the shore is mostly rock and black sand. Nauthólsvík, with its geothermally warmed lagoon and hot tub, makes a fun hour, but the real swimming happens in the heated pools.

Copenhagen is the far better place to eat. It helped redefine Nordic cooking at the top end, and below that sits a deep everyday food culture: smørrebrød lunches, cardamom buns, the Torvehallerne market halls, and the natural wine bars and breweries of Vesterbro and Nørrebro.

Reykjavik cooks with excellent ingredients, from Arctic char and langoustine to lamb and skyr, and a bowl of lamb soup or plokkfiskur makes a good lunch. But the choice around Laugavegur and the Old Harbour soon runs out, and the prices send many visitors back to the supermarket.

Copenhagen has three or four days of sights. There is Rosenborg with the crown jewels, the rococo palaces of Amalienborg, Christiansborg above its medieval ruins and the gabled quays of Nyhavn, along with solid museums such as the National Museum and the Glyptotek.

Reykjavik's list is short. Hallgrímskirkja, Harpa, the Sun Voyager and the Settlement Exhibition, built around a Viking-age longhouse, fill a day or two, and most visitors use the city as a base rather than a destination.

Copenhagen gives you a longer and more varied night out. There are bars in the converted butchers' halls of Kødbyen, scruffier places along Blågårdsgade and Jægersborggade, a good cocktail scene, and summer evenings drinking beside the canals.

Reykjavik packs its weekend into a few blocks around Laugavegur, where the runtur moves between small bars that turn into dance floors after midnight. It is friendly and memorable in the midsummer half-light, but quiet midweek and short on variety.

This is Reykjavik's great advantage. The rift valley at Þingvellir, the Strokkur geyser and Gullfoss are an hour or two away, and beyond them lie the south-coast waterfalls, glacier walks and the steaming lava fields of Reykjanes. Closer in you can climb Mount Esja or take a whale-watching boat from the Old Harbour. Summer brings endless daylight for hiking, and winter the chance of the northern lights.

Copenhagen's outdoors is gentle by comparison: deer among the oaks of Dyrehaven, an easy cycle up the Øresund coast and kayaking in the harbour. The nearest real drama is the chalk cliffs of Møns Klint, about two hours away.

A day out from Copenhagen usually means a short train ride with a castle, a cathedral or a museum at the end of it. Kronborg at Helsingør, the castle behind Hamlet's Elsinore, is under an hour north, and Frederiksborg and the Louisiana museum can go on the same line. Roskilde has its royal burial cathedral and Viking ships, and Malmö and Lund are just across the bridge in Sweden.

From Reykjavik, a day out is a long drive through empty country with a few stops on the way. Þingvellir, where the Viking-age parliament met in the open air, is the one great historic site. Skálholt, Reykholt and the wooden merchant houses of Eyrarbakki break up the road, but none of them is worth the journey on its own.

Copenhagen is the easier city with children. Tivoli sits beside the central station, and the aquarium, the zoo, Experimentarium and the old Bakken fairground add plenty more. Prams on the metro and cargo bikes everywhere show a city built around family life.

Reykjavik is safe and welcoming too, and children love its outdoor pools with slides and hot tubs, even in snow. The catch is that the big sights mean long coach days, and the weather and the cost of meals wear harder on a family.

Copenhagen is simpler in every way. The centre is flat and walkable, the driverless metro runs all night and reaches the airport in about a quarter of an hour, and separated bike lanes make cycling the obvious way to get about.

Reykjavik's centre is small enough to walk, but buses are infrequent, there is no rail of any kind, and the airport is about 45 minutes away by coach. To see the landscape you need a hire car or a tour, and in winter ice and early darkness make even short walks harder.

Copenhagen is a proper shopping city, especially for design. There are furniture and lighting shops, the Royal Copenhagen porcelain flagship on Amagertorv, Strøget and the old department stores Illum and Magasin du Nord, and Scandinavian fashion and vintage in the Latin Quarter and Nørrebro.

In Reykjavik, shopping fills an afternoon along Laugavegur and Skólavörðustígur. A hand-knitted lopapeysa, outdoor clothing and ceramics or jewellery made from lava stone and fish leather are worth buying, but the range is small.

Both are among the most expensive places in Europe, but Copenhagen is the less painful of the two. Hotels and restaurants cost a lot, yet free sights such as Nyhavn, the parks and the harbour baths help, as do reasonably priced transport and bakery lunches.

Reykjavik costs more at almost every turn, from guesthouses and plain meals to alcohol, tours, car hire and fuel. Cheap pools, superb tap water and self-catering make a difference, but you have to budget high from the start.

For a night of opera, ballet or orchestral music, Copenhagen gives you far more choice. The Royal Danish Theatre runs the Opera House on the harbour, the Old Stage and the Playhouse, the Royal Danish Ballet keeps the Bournonville tradition alive, and DR Koncerthuset in Ørestad is an outstanding concert hall. Jazz clubs, the July jazz festival and summer concerts at Tivoli add to the year.

Reykjavik does well for a city of its size. The Iceland Symphony Orchestra plays at Harpa, and the city's alternative and electronic scene is well known, peaking during Iceland Airwaves in late autumn. Outside the festivals, though, there is little choice on any given night, and in both cities most theatre is in the local language.

Reykjavik is made for soaking. Every neighbourhood has a geothermal outdoor pool with hot tubs and a cold plunge, and locals use Laugardalslaug and Vesturbæjarlaug in any weather. The Blue Lagoon lies in the Reykjanes lava fields, and there are quieter hot springs along the Golden Circle.

Copenhagen's version is Nordic hot and cold bathing rather than thermal water. You sweat in wood-fired saunas floating in the harbour and then plunge into the sea, and the city's calm pace, with its lakes, gardens and long coffees, does the rest. It is restful, but there are no hot springs.