Copenhagen or Gdansk?

Neither is a beach destination, and the sea is equally cool in both, so the difference lies in the kind of swim. In Copenhagen it is part of city life: you can jump off a wooden harbour bath at Islands Brygge, or take the metro to the man-made lagoon beach at Amager Strandpark or out to Bellevue.

Gdansk has the more natural shoreline, a near-continuous run of fine, pale sand from Brzeźno and Jelitkowo to Sopot, with pine-backed Stogi and the Hel Peninsula further out. Its shallow, gentle water is kinder to small children than Copenhagen's harbour baths.

Copenhagen is a food destination in a way Gdansk is not. Its New Nordic restaurants draw travellers in their own right, and below them are rye smørrebrød, cardamom buns, the Torvehallerne halls and serious coffee and natural wine in Vesterbro and Nørrebro.

Gdansk feeds you well and cheaply rather than memorably: pierogi, żurek, herring and smoked Baltic fish, Kashubian country cooking and milk-bar canteens. The tourist restaurants along Długa are uneven, so the better meals are found in Wrzeszcz, the shipyard area, Sopot and Gdynia.

The two are close, but the history they tell is very different. Copenhagen is royal and maritime: Rosenborg's crown jewels, the guard at Amalienborg, parliament on Slotsholmen, Nyhavn's gables, and modern Danish architecture along the harbour, with solid rather than world-famous museums such as the Glyptotek and the National Museum.

Gdansk combines a rebuilt Hanseatic merchant town, with the Long Market, the medieval crane and the vast brick bulk of St Mary's, with some of Europe's most powerful twentieth-century sites. The Museum of the Second World War, Westerplatte and the European Solidarity Centre give it a weight Copenhagen's palaces do not have.

Copenhagen has the somewhat livelier nights, and they are concentrated: the converted butchers' halls of Kødbyen, scruffier bars on Blågårdsgade and Jægersborggade, good cocktails in the centre and long, light summer evenings on the canals. Drinks are expensive, though, and weeknights are quiet.

In Gdansk going out is spread across the Tricity, with Main Town pubs, student bars in Wrzeszcz and warehouse parties in the shipyard. In summer it all moves to Sopot's Monte Cassino street, with trains running late, but outside the warm months it is noticeably quieter.

Gdansk has more to offer outdoors. Beech-wooded hills with ravines and marked trails rise right behind Oliwa and Sopot, the Kashubian lakes are about an hour away for canoeing and cycling, and the Bay of Puck behind the Hel dunes is excellent kitesurfing water.

Copenhagen's green space is gentler and flatter: deer among the oaks of Dyrehaven, the Øresund coast road by bike, and paddling in the harbour. The nearest real drama, the chalk cliffs of Møns Klint, is about two hours away.

Copenhagen's outings are richer and easier to string together. Kronborg at Helsingør, moated Frederiksborg and the Louisiana museum all sit on one northern rail line, Roskilde has its Viking ships, and Malmö and Lund in Sweden are a short train ride over the bridge.

Gdansk has one outstanding trip in Malbork, the Teutonic Knights' huge brick fortress, and a good second tier in Sopot, Gdynia, Pelplin abbey and Copernicus's Frombork. Torun's Gothic old town rewards a long day, but the range is narrower overall.

Copenhagen works with children in any season, because much of what it offers is indoors or close by: Den Blå Planet near the airport, the hands-on Experimentarium and the large, well-kept zoo in Frederiksberg, with the old Bakken fairground in Dyrehaven for a summer afternoon. Playgrounds in every park and calm streets that feel safe at any hour make ordinary days simple, though grey skies cut outdoor time short for much of the year and there is no big theme-park resort.

Gdansk is at its best with children in summer, when the beaches, the zoo in the wooded hills at Oliwa and boat trips to Westerplatte or the Sopot pier fill the days. Gdynia's pier aquarium and science centre and the Hevelianum in its hilltop fort cover wet afternoons, but once the cold and wind arrive these indoor places are most of what is left.

Both have flat, walkable historic centres, but Copenhagen is easier beyond them. Its metro runs around the clock and reaches the airport quickly, one ticket covers trains, buses and harbour buses, and its separated bike lanes make cycling the natural way to get about.

In Gdansk the Main Town is all on foot, and the SKM commuter line and trams handle the rest simply and cheaply. The effort is distance, since Sopot and Gdynia stretch some 30km along the coast.

Copenhagen is a real shopping city for anyone who loves design. It has furniture, lighting and ceramics shops, Royal Copenhagen porcelain on Amagertorv, Strøget, the old department stores Illum and Magasin du Nord, and independent Scandinavian labels in the Latin Quarter and Nørrebro.

Gdansk has one speciality, Baltic amber, sold in the jewellers and workshops of Mariacka Street, and otherwise mainly malls and chains. The medieval St Dominic's Fair adds summer craft and antique stalls, the kind of market Copenhagen largely lacks.

The gap is wide. Copenhagen is among Europe's most expensive cities, with costly rooms, meals and drinks, and saving money there means supermarket lunches, picnics and free sights like the parks and harbour baths.

Gdansk costs far less for meals, beer, coffee, transport and museums. The one exception is rooms in July and August, when coastal demand pushes up prices in the Main Town and Sopot, so late spring or early autumn gives the best value.

Copenhagen has the deeper stage. The Royal Danish Ballet keeps the Bournonville tradition alive, opera plays at the harbourfront Opera House, DR Koncerthuset is an outstanding concert hall, and the July jazz festival fills squares across the city.

Gdansk has a respectable season, with the Baltic Opera, the Philharmonic in its converted power station and an opening-roof Shakespeare Theatre, along with organ recitals in Oliwa Cathedral and a big summer rock festival in Gdynia. In both cities, visitors are better off with music than with theatre in the local language.

Both cities practise cold-water bathing, but Copenhagen has made it a full ritual. Wood-fired saunas float in the harbour and stand on the beaches, people plunge into cold water all winter, and the calm city, its lakes and palace gardens make slow days easy.

Gdansk's version is morsowanie, locals wading into the icy Baltic on winter weekends. Beyond that, its wellness rests on the spa floors of Sopot's grand seafront hotels and a few day spas, pleasant for an afternoon but thinner overall.