Hamburg or Lubeck?

Lübeck wins here because it has its own seaside. Travemünde has a long sandy beach with wicker chairs, the Baltic there is calm and shallow enough for small children, and Timmendorfer Strand and Scharbeutz are a short ride up the bay.

Hamburg's riverside sand at Oevelgönne and Blankenese is for watching container ships at sunset, not swimming, because currents and ship wash make the Elbe unsafe. Visitors from Hamburg who want to swim end up on the same Lübeck Bay beaches, about an hour away. The water is equally cool for both.

Hamburg eats more broadly. You can have a fish roll at the Landungsbrücken, Labskaus and eel soup, a Franzbrötchen with coffee in Ottensen, and then choose from Portuguese and Turkish places near the harbour or a proper fine-dining meal.

Lübeck's table is smaller but has a clearer character of its own. It has centuries of marzipan in the cafés by the town hall, Rotspon wine aged in the city's cellars, and herring and plaice served in the old sea captains' guild house. Beyond those specialities the choice soon becomes ordinary provincial dining.

Lübeck has the more complete historic town. Almost the whole island old town is UNESCO-listed, with the Holstentor, the Marienkirche and seven brick spires, and its stepped-gable houses and hidden courtyards are made for slow wandering. The Hansemuseum and the Buddenbrookhaus round it off, and two days covers it.

Hamburg's heritage is spread across districts, because the war destroyed most of its old core. Its strengths are the canals and warehouses of the Speicherstadt, the Chilehaus and the harbour views from the Elbphilharmonie plaza. It also has the bigger art collections, especially the Kunsthalle's run from old masters to Caspar David Friedrich.

This is the biggest gap between the two. Hamburg goes out until dawn, from the neon, cabaret and music clubs of the Reeperbahn to the alternative bars of the Schanzenviertel and the smarter places around the Alster.

Lübeck offers a glass of wine by the Obertrave, a pub in the old town or a summer evening on Travemünde's promenade, and little after midnight. Locals who want a big night take the train to Hamburg.

Both sit in flat northern country, and they are broadly level outdoors. The difference is that Hamburg's outdoors is inside the city, while Lübeck's lies at its edges. In Hamburg you can sail or paddle on the Alster, walk the Elbe path up to Blankenese's wooded bank, or cycle through the Altes Land orchards when they blossom in spring.

Lübeck puts you closer to open countryside. You can canoe the reed-lined Wakenitz towards the Lauenburg lakes, walk the clay cliff of the Brodtener Steilufer above the sea, or head for the Holstein Switzerland lakes within the hour.

Hamburg is the better base. Lübeck itself, Lüneburg's leaning gabled houses, Bremen, Schwerin, Celle and Stade are all an easy train ride away, so you could fill a week without repeating yourself.

Lübeck's list starts with Hamburg, which is worth a full day, and Wismar and Schwerin to the east. After the lake towns of Ratzeburg, Mölln and Eutin, the choice runs out sooner.

Hamburg keeps children busy in any weather. Miniatur Wunderland's model airports and harbours, Tierpark Hagenbeck's open enclosures and aquarium, harbour ferries and the old Elbe tunnel, and the Stadtpark planetarium make rainy days easy to plan.

Lübeck works well with children in summer. The small, safe old town pairs nicely with Travemünde's shallow beach, and Hansa-Park is only half an hour up the coast. Outside the warm months there is much less aimed at children, and the museums have to fill the gaps.

Hamburg runs on trains and ferries, Lübeck on foot. In Hamburg the U-Bahn and S-Bahn reach every district a visitor is likely to want, the airport is on the S-Bahn, and the harbour ferries run on the same ticket, so a crossing of the Elbe doubles as a sightseeing trip. Even Blankenese or Hagenbeck is a single train ride, which makes it the more effortless city once you range beyond the centre.

Lübeck's old town is an island about 2km long, largely pedestrianised with some cobbles, and the station sits just across the river from the Holstentor, so inside the town you hardly need transport at all. Beyond it the network is thinner: city buses and the regional train to Travemünde, about twenty minutes away, cover the essentials, but the lakes and small coastal villages are easier with a car.

Hamburg is a proper shopping destination. Luxury labels line Neuer Wall, covered arcades run off the Jungfernstieg, and the Alsterhaus department store anchors the area. The Karolinenviertel and Schanzenviertel add vintage and streetwear, and the old trading houses sell tea and coffee.

Lübeck has a chain-store spine on Breite Strasse and Königstrasse and a few craft shops and galleries in the courtyard passages. Marzipan is the souvenir to take home. For fashion, people go to Hamburg.

Lübeck is the cheaper stay. It has a good spread of moderately priced guesthouses and mid-range hotels in the old town, taverns and fish kiosks that don't stretch the budget, and inexpensive trains to the coast. The exception is Travemünde and the bay resorts in July and August, which cost more and book up early.

Hamburg's rooms and central restaurants are priced for one of Germany's wealthiest cities, and trade fairs push them higher. A day ticket that includes the ferries, the free Elbphilharmonie plaza and cheap fish rolls in Altona help keep costs down.

Hamburg is far ahead, and its stages are a reason to go in their own right. It has the Elbphilharmonie and the Laeiszhalle for concerts, the State Opera and the internationally known Hamburg Ballet, the Schauspielhaus and Thalia for theatre, and large musical theatres across the harbour. St Pauli's small rock clubs, where the Beatles started out, keep going late.

Lübeck has a respectable season at its Art Nouveau Theater Lübeck. Its real distinction is organ music in the Marienkirche, where Buxtehude once played, along with summer concerts of the Schleswig-Holstein Music Festival.

Neither city is a spa destination, and they are broadly level. Hamburg relaxes in the German sauna tradition, with the art nouveau Holthusenbad and large bath complexes, or with a slow boat ride around the Alster and an hour in the Japanese garden at Planten un Blomen.

Lübeck's calm comes from the sea air. Travemünde has been a seaside spa resort since the early nineteenth century and has wellness hotels and the seawater pools at Scharbeutz nearby. The old town is quiet enough that simply sitting by the river does the job.