Copenhagen or Stockholm?

Neither city is a beach destination, and in both the swimming is an add-on to a summer stay, but the shoreline is different. Copenhagen offers sand: the long lagoon beach at Amager Strandpark, the classic Bellevue strand to the north, and wooden harbour baths at Islands Brygge in the middle of town.

Stockholm swims from rock slabs, jetties and small lawns, at Långholmen, on Kungsholmen and in the freshwater lakes at Hellasgården, with archipelago coves a ferry ride further out. Choose Copenhagen for towel-on-sand days, and Stockholm for diving off warm granite.

Copenhagen is the stronger city for eating. Its foraging and fermentation kitchens are a reason to travel in their own right, and the everyday layer is just as good, with smørrebrød on rye, bakeries everywhere, Torvehallerne's stalls and harbourside street-food markets in summer.

Stockholm has a serious tasting-menu scene too, but its character lies in husmanskost, meatballs with lingonberries and fried herring in old dining rooms, plus the slow ritual of fika. Street food is thin beyond the hot-dog kiosks, and takeaway alcohol is sold only in state shops, which makes casual grazing less easy than in Copenhagen.

These two are closely matched, with the difference lying in what you see. Copenhagen's heritage is royal and maritime: the crown jewels at Rosenborg, the guard changing at Amalienborg, the gabled houses of Nyhavn and harbourside modern architecture, with museums that are good rather than famous.

Stockholm edges ahead on singular sights. The Vasa warship from 1628 and Skansen, the first open-air museum, have no real equal, and Gamla Stan's medieval lanes give it an old town Copenhagen lacks. Its sights are spread across islands, so seeing them means crossing bridges and taking ferries.

Nights out are roughly equal in both cities, and both are pricey and quiet midweek. Copenhagen's centre of gravity is Kødbyen, where bars and small clubs share old meatpacking halls, backed by scruffier Nørrebro streets and a strong cocktail scene.

Stockholm splits more sharply: polished, strict-door clubs around Stureplan, and relaxed pubs and wine bars on Södermalm. In summer both move outdoors, to the canals of Nyhavn and Christianshavn in Copenhagen, and to the waterfront terraces under Stockholm's barely dark skies.

This is where Stockholm pulls clearly ahead. Tens of thousands of granite islands begin at the city's edge, Tyresta National Park and Nackareservatet are under an hour away by public transport, and kayaking, sailing and island hikes are ordinary summer outings. In a cold winter there is even skating on natural ice.

Copenhagen's outdoors are gentler and closer to parkland: deer among the oaks of Dyrehaven, the open common of Amager Fælled, and a flat coastal ride towards Helsingør. Its nearest dramatic scenery, the chalk cliffs of Møns Klint, is about two hours away.

Both cities give plenty of good excursions, but the way you travel differs. Copenhagen's are by train and work all year: Kronborg at Helsingør, Frederiksborg and the Louisiana art museum on one line, Roskilde's Viking ships, and Malmö and Lund across the bridge, so you get a second country without effort.

Stockholm leans on boats. Drottningholm, Birka, Gripsholm and the archipelago villages of Vaxholm and Sandhamn are summer voyages, and in winter the list falls back to rail trips such as Uppsala and Sigtuna.

Copenhagen spreads its children's sights across the city and its edges. Tivoli's wooden rides and evening lights are by the central station, Den Blå Planet is near the airport and the zoo is in Frederiksberg. Experimentarium and the old Bakken fairground are a short train ride north. Prams on trains and cargo bikes everywhere make it easy to get between them.

Stockholm keeps its best on a single island. On Djurgården, Skansen's moose, bears and seals, the Astrid Lindgren train ride at Junibacken, Gröna Lund's rides and the Vasa are all within walking distance. The ferry over is a treat for children in itself. Both cities are just as easy with children day to day, and long, dark winters cut down outdoor days in both.

Copenhagen is the easier city to cover on foot or by bike. The centre is compact and flat, and cycling is the obvious way to get about, on separated lanes with their own traffic lights. The driverless metro runs all night and reaches the airport in about a quarter of an hour.

Stockholm's fourteen islands give it a different pace, with bridges between districts, steep streets up Södermalm and commuter ferries to Djurgården that double as sightseeing. Its painted metro stations, carved from the bedrock, are worth seeing in themselves, and cycling is good in summer but harder on winter ice. Neither city needs a car, and each uses one ticket across its whole network.

Both are design capitals, but they lean different ways. Copenhagen is stronger for homeware: lighting, furniture, ceramics and the Royal Copenhagen flagship on Amagertorv, with Strøget and the old department stores tying it together, though luxury fashion is limited.

Stockholm is the better choice for clothes, with minimalist Swedish labels and the luxury houses around Biblioteksgatan, the grand NK store, and a deep vintage and second-hand culture in SoFo. Neither has much in the way of markets.

Both are expensive, but Copenhagen is the harder on the budget, with costly hotel rooms even in the mid-range and steep prices for eating and drinking at every level. Savings come from bakeries, supermarket picnics by the lakes and a bike instead of taxis.

Stockholm is dear too, but it gives you more room to save. Hotels drop at weekends and through July, when business travel stops, the weekday lunch deal is a filling meal at a fair cost, and a multi-day transport pass is good value.

The formal stages in the two cities are about equal, and in both most drama is in the local language. Copenhagen's highlights are the Royal Danish Ballet's Bournonville tradition, the harbourfront Opera House, the acoustics of DR Koncerthuset and a jazz heritage that fills squares and courtyards every July.

Stockholm's rarest offer is baroque opera at the Drottningholm Palace Theatre, on its original eighteenth-century stage machinery, alongside the Royal Opera and the Philharmonic at Konserthuset. Its pop and arena scene is strong, but high summer is quieter.

Copenhagen's bathing is outdoor and informal. Wood-fired saunas float in the harbour and stand by the beaches, the sea baths at Kastrup and Amager Strandpark join in, and the routine ends with a jump into cold water, even in winter. Beyond that there are only a handful of day spas.

Stockholm is better for a classic spa day. Centralbadet, an Art Nouveau bathhouse from 1904, and the older Sturebadet are in town, and waterside spa hotels in Nacka and the inner archipelago are under an hour away. It shares the Nordic habit of a hot sauna and a cold dip, at Hellasgården through a hole in the ice. Neither city has thermal springs, and both are calm enough for slow afternoons.