Oslo or Copenhagen?

Neither is a beach destination, and the swimming is about equal. What differs is the setting. Copenhagen's swimming is urban and sandy: harbour baths at Islands Brygge for a midday dip, the long man-made beach at Amager Strandpark a few metro stops out, and Bellevue's whitewashed lifeguard towers on the Øresund.

In Oslo a swim means a short journey. Harbour ferries carry you to Hovedøya and Langøyene for rocks and small coves, Bygdøy has Huk and Paradisbukta, and the metro runs out to the forest lake at Sognsvann. A swim there feels like a trip into nature rather than a stop on a city walk.

Copenhagen is the stronger food city by some way. Its fine dining helped redefine Nordic cooking, but its real advantage is everyday food: smørrebrød on rye at lunch, cardamom buns from corner bakeries, the Torvehallerne market halls and harbourside street food in summer.

Oslo cooks with similar cold-water produce and has its own tier of tasting menus, but the middle ground is mostly brunch places and international bistros, and there is little street food. Its strongest suits are light-roast coffee, found almost everywhere, and prawns eaten on the quay in summer.

Copenhagen has the edge because it pairs its museums with an old townscape. Rosenborg holds the crown jewels, the guard changes at Amalienborg, Christiansborg stands over medieval ruins, and the gabled houses of Nyhavn line the canal. You feel the royal capital simply by walking its streets.

Oslo's centre has little old architecture, so its appeal lies in particular places: the Munch Museum and The Scream, the Fram and Kon-Tiki on Bygdøy, and the granite crowds of Vigeland Park. These are memorable, but there are fewer of them, and two or three days covers the city where Copenhagen rewards three or four.

Copenhagen gives the better night out. Kødbyen's old butchers' halls hold bars and small clubs that run until morning at weekends, Nørrebro adds a younger and scruffier bar crowd, and the cocktail bars in the centre are good.

Oslo suits a relaxed drink in Grünerløkka or around Youngstorget more than a big night. Bars close around three, and alcohol is so expensive that locals drink at home before going out. In both cities weeknights are quiet, and summer evenings move out to the waterfront.

Oslo is far ahead here. The metro climbs to Holmenkollen and Sognsvann, where Nordmarka's forest, lakes and cabins begin, and in winter the same trails become floodlit cross-country ski tracks. Downhill slopes and a toboggan run can be reached by public transport, and the fjord adds islands and skerries for sailing and kayaking.

Copenhagen is flat and mild by comparison. Dyrehaven's deer and old oaks, the coastal ride towards Helsingør and paddling in the harbour make pleasant afternoons, but the nearest dramatic scenery is the chalk cliffs of Møns Klint, about two hours away.

Copenhagen has more day trips, and better ones. Kronborg, Frederiksborg and the Louisiana museum all lie on the train line north, Roskilde's cathedral and Viking ships are half an hour west, and Malmö and Lund put a day in Sweden within easy reach across the bridge.

From Oslo the outings are pleasant rather than compelling: the star-shaped fortress town of Fredrikstad, wooden Drøbak by boat, and Lillehammer's ski jumps a couple of hours north. The fjord scenery most people picture when they think of Norway is too far away for a day trip.

Copenhagen is among the easiest capitals for children, and it has the big attractions Oslo lacks: Tivoli beside the station, Den Blå Planet, the Frederiksberg zoo, Experimentarium and the old Bakken fairground in the deer park.

Oslo is just as calm and easy with a pram, and Bygdøy makes a very good family day, with farm animals at the Folk Museum and a polar ship to climb aboard at the Fram. Beyond that it relies on the outdoors, such as the Opera House roof, the island ferries and winter sledding, with Tusenfryd as its one amusement park.

Both are easy without a car, with walkable centres and a single ticket for all public transport, but you get around them differently. Copenhagen is a cycling city: flat, with separated bike lanes, plus a driverless metro that runs through the night and reaches the airport in about a quarter of an hour.

Oslo relies on trams and a metro that climbs into the forested hills, with island ferries included in the same network and a bus or summer boat out to Bygdøy. In winter the pavements can be icy, so pack good shoes.

Copenhagen is the better shopping trip, mainly for design. Furniture, lighting and ceramics shops cluster in the centre, Royal Copenhagen has its flagship on Amagertorv, Strøget runs from chain stores to luxury labels, and Illum and Magasin du Nord are worth seeing as institutions.

Oslo is smaller in scope: Karl Johans gate for the chains, Steen & Strøm for Nordic brands, Grünerløkka for vintage and records. Its strength is practical things to take home, such as patterned knitwear, outdoor clothing and woollen blankets. Neither city has much in the way of markets.

Both are among the most expensive cities in Europe, and there is little to choose between them. Oslo bites a little harder on alcohol and taxis, while in Copenhagen transport is reasonable and a bicycle replaces most taxi rides.

The ways to save are the same in both: bakery or supermarket lunches, picnics and the free sights. In Copenhagen those are Nyhavn, the harbour baths and the lakes; in Oslo, Vigeland Park, the Opera House roof, the forest trails and the fjord islands.

Copenhagen has a little more on. The Royal Danish Ballet keeps the Bournonville tradition alive across the Royal Danish Theatre's three stages, DR Koncerthuset is an outstanding concert hall, and the July jazz festival fills squares and courtyards.

Oslo's centrepiece is the Opera House, where an evening of opera or ballet in the oak-lined hall is a highlight of any visit, and the Oslo Philharmonic is well regarded. Its August festival in Tøyen park is the big summer draw. In both cities most theatre is performed in the local language, so visitors tend to book music and dance.

The two share the Nordic way of relaxing: a wood-fired sauna, then cold water, all year round, with no thermal springs and few serious spas. Copenhagen spreads the habit across its harbour baths and the beach saunas at Amager Strandpark and Kastrup, and adds slow afternoons by the lakes, palace gardens and canals.

In Oslo the sauna is more central to daily life. Sociable floating saunas sit beside the Opera House and at Sørenga, with a ladder straight down into the fjord, and they are easy for a visitor to join.