Berlin or Copenhagen?

Neither city is a beach destination, and swimming in both is a summer extra rather than a reason to go. The difference is in the water. Berlin swims in lakes: the sandy lido at Wannsee, the Müggelsee and small forest lakes like Schlachtensee, which warm up nicely in high summer.

Copenhagen swims in the sea and the harbour. You can jump off the wooden baths at Islands Brygge in the city centre or take the metro to the Øresund sand at Amager Strandpark, but the water stays noticeably cooler than Berlin's lakes.

Copenhagen is the better food city. It helped redefine Nordic cooking, and its fine dining based on foraging and fermentation draws people on its own. Its everyday food is just as good: smørrebrød on rye, cardamom buns and the Torvehallerne halls by Nørreport.

Berlin's strength is range rather than a cuisine of its own. Turkish grills and bakeries in Kreuzberg and Neukölln, good Vietnamese and Korean cooking, and street-food evenings at Markthalle Neun make it more casual and much cheaper, if less distinctive.

Berlin carries far more weight here. Museum Island, with Nefertiti and the Pergamon collections, and the old masters at the Gemäldegalerie are world-class on their own. The Reichstag, the Holocaust Memorial and the Wall Memorial on Bernauer Strasse let you see twentieth-century history in the places where it happened.

Copenhagen's heritage is smaller and prettier: the crown jewels at Rosenborg, the guard changing at Amalienborg, and the gabled houses of Nyhavn. Its museums are good but not famous, and three or four days covers them, whereas Berlin can fill a week.

This is where the two differ most. Berlin is one of the world's great club cities. Techno runs in old power stations and warehouses from Saturday night into Monday, with strict doors, and bars stay open almost round the clock across Friedrichshain, Kreuzberg and Neukölln.

Copenhagen goes late at weekends too, with bars and small clubs in the old Meatpacking District and good cocktail bars in the centre. Midweek is quiet, drinks are expensive, and nobody plans a trip around its clubs the way they do in Berlin.

Both cities are flat and green, with no hills to climb, so the outdoors here means easy walking, cycling and paddling. Berlin has more space for it: the Grunewald and the Havel lakes, the old Tempelhof runways for cycling and skating, the Wall Trail around the former West, and Brandenburg's lakes for canoeing.

Copenhagen has the sea instead. You can cycle the Øresund coast road, walk among the deer in Dyrehaven and kayak the harbour canals. Møns Klint's chalk cliffs are the nearest dramatic scenery.

Copenhagen has the wider choice. Kronborg, Frederiksborg and the Louisiana art museum all lie on the line north and can share a day. Roskilde has its cathedral and Viking ships, and Malmö and Lund in Sweden are only a short train ride over the bridge.

Berlin has one excellent outing in Potsdam's palaces at Sanssouci, plus Wittenberg, Leipzig and the Spreewald. Dresden takes a long day there and back, though, and after those the options thin out.

Copenhagen is the easier city with children. Tivoli, with its old wooden rides, is right by the station, and the aquarium, the zoo, Experimentarium and the old Bakken fairground are all close. The streets are calm, and families ride everywhere in cargo bikes.

Berlin does well too, with two large zoos, the dinosaur at the Natural History Museum and the trains and planes at the Museum of Technology. Its sheer size means more time on public transport, and many of its key sights are heavy going for young children.

Both are flat, easy to cycle and well served by integrated public transport, so neither needs a car. The difference is scale. Copenhagen's sights, from Nyhavn to Rosenborg, are a short walk apart, and the driverless metro runs all night to the airport.

Berlin is a set of separate centres in Mitte, Kreuzberg, Prenzlauer Berg and Charlottenburg. Each is walkable, but you need the U-Bahn, S-Bahn or trams to get between them, though weekend night trains make late returns simple.

There is little to choose between them overall, but they suit different shoppers. Berlin is the city for rummaging: the Sunday flea markets at Mauerpark and Boxhagener Platz for vinyl and East German curios, vintage shops in Kreuzberg, and the KaDeWe food hall.

Copenhagen sells design. Its furniture, lighting and ceramics shops, the Royal Copenhagen flagship on Amagertorv and Scandinavian labels in the Latin Quarter are the reason to bring an empty suitcase. Markets are its weak spot.

Berlin is far cheaper. Hotels cost less than in most big capitals, and döner, Vietnamese canteens and Kneipe beer keep daily spending low, although museum-heavy days still add up.

Copenhagen is one of Europe's most expensive cities at every level, from mid-range rooms to a beer at the bar. Its free harbour baths, parks and Nyhavn help, as do bakery lunches and a rented bike, but a trip of the same length will cost noticeably more.

Berlin offers more on stage. It has three full opera houses and the Berlin Philharmonic in Scharoun's Philharmonie, the Friedrichstadt-Palast revue for those who don't speak German, and jazz cellars and experimental venues behind them.

Copenhagen has fine institutions on a smaller scale: the Royal Danish Ballet and its Bournonville tradition, the harbourfront Opera House and the acoustics of DR Koncerthuset. Its jazz clubs give it a particular edge, and the July jazz festival fills the squares.

Both are equally good for unwinding, and both sweat rather than soak, since neither has hot springs. Berlin follows the German sauna tradition, with large clothes-free complexes, ritual infusions and the columned halls of Stadtbad Neukölln, and Brandenburg's thermal resorts are about an hour out.

Copenhagen's version is wood-fired saunas floating in the harbour and on the beaches, with a cold-water plunge afterwards, all year round. It suits people who like that hot and cold contrast more than indoor rest rooms.