Frankfurt or Luxembourg?

Neither city has a beach, and nobody should pick either for swimming. Luxembourg has a little more to offer on a hot day. The Upper Sûre reservoir has several bathing spots along its wooded shores, and the gravel-pit lakes at Remerschen sit in the Moselle valley.

Frankfurt has one main lake, the sandy-shored Langener Waldsee in the forest to the south, and otherwise relies on outdoor pools, since the Main is not for swimming.

The two eat about equally well, but in different ways. Frankfurt's pleasure is homely and cheap: shared tables in Sachsenhausen's apple-wine taverns, Grüne Soße and Handkäs, the Kleinmarkthalle, and a run of global kitchens in the Bahnhofsviertel.

Luxembourg leans more towards fine dining, with French cooking at the top and Portuguese and Italian places in the neighbourhoods. Its real draw is Moselle wine, especially Riesling and crémant by the glass, but casual eating is thinner and lunch is the meal to plan around.

These two are broadly level, but the appeal is different. Frankfurt is a museum city: the Städel has real international standing, and more than a dozen institutions line the Main beside a rebuilt Römer and the only true skyline of towers in Germany.

In Luxembourg, the city itself is the sight. The UNESCO-listed fortress, the casemate tunnels and the view from the Chemin de la Corniche down to the Grund are the attraction, with the palace, the cathedral and MUDAM as additions. Choose Frankfurt for galleries, and Luxembourg for townscape.

Frankfurt is clearly the place for a night out. It shares with Offenbach a real place in techno and house history, and its clubs still carry that on at weekends, with the Bahnhofsviertel's cocktail bars, Berger Straße's neighbourhood bars and the crowded summer riverbanks around them.

Luxembourg's evenings are smaller and earlier. The Rives de Clausen and the Grund's stone pubs are pleasant, but Thursday and Friday are the busy nights, and many residents leave at weekends. That is exactly when Frankfurt comes alive.

There is little to choose between them overall, though the landscapes differ. Luxembourg's green runs right through the centre, with wooded gorges below the old town. The Müllerthal's sandstone gorges and narrow rock passages, half an hour away, have more texture than anything near Frankfurt.

Frankfurt's countryside is gentler and wider: the beech-forested Taunus up to the Großer Feldberg, the large Stadtwald, and long, flat cycle paths along the Main towards the Rheingau vineyards.

Both are good bases, but Frankfurt's rail connections give it far more range. Heidelberg and the castle-lined Rhine Gorge are about an hour away, Cologne's cathedral is the same by high-speed train, and Mainz, Wiesbaden and Darmstadt are closer still. That is enough for a week of outings.

Luxembourg makes up for its size with its position on three borders. Roman Trier and Gothic Metz are each under an hour away, while Vianden's castle, Echternach and the Moselle wine villages fill the closer days. The list simply runs out sooner.

Frankfurt has much more that is made for children. The dinosaur hall at the Senckenberg, a central zoo, the Palmengarten's glasshouses and boat trips past the towers will fill several days, with a wildlife park and a fairy-tale park out in the Taunus.

Luxembourg is calm, safe and easy with a buggy, and children love the casemate tunnels. Beyond that there is the small Parc Merveilleux and no zoo or aquarium, so it suits a quiet two or three days rather than a school vacation week.

Both are easy to get around, and both have compact centres you can walk. Luxembourg is the simpler of the two, because trams, buses and trains are free across the country, and public lifts and a funicular handle the climb between the levels of the city.

Frankfurt's integrated network reaches further, to the Taunus, Mainz and Wiesbaden, but its zones take some learning. It wins on arrivals, with the airport about a quarter of an hour from the centre and the main station on the high-speed lines.

Frankfurt is the better place to shop. The Zeil covers department stores and malls, Goethestraße has the luxury houses, and Berger Straße and Schweizer Straße have the independent boutiques, delis and design shops that Luxembourg largely lacks.

Luxembourg's Grand-Rue is mostly premium brands for a wealthy local clientele. The things worth carrying home are Villeroy & Boch porcelain from the factory outlet and bottles of crémant.

Neither is a budget destination, but Frankfurt costs noticeably less. Its high prices are mostly in the hotels, and those drop at weekends and in summer when there is no trade fair. Taverns, Turkish grills and market stalls keep meals cheap.

In Luxembourg, both rooms and eating out run above the Western European norm. Free transport, free museums and lunch menus help, and some visitors sleep in Trier or Metz and come in by train for the day.

Frankfurt has a deeper programme that is its own. Its opera company is one of Germany's most respected and known for adventurous productions. The Alte Oper, the Schauspiel, Mousonturm's dance and old jazz cellars complete a season that runs from autumn to early summer.

Luxembourg's Philharmonie is a superb hall with its own orchestra, but most of what plays at the Grand Théâtre is visiting work. Its summer open-air concerts at Neimënster do fill the months when Frankfurt goes quiet.

The two are broadly level, and neither has a bathing culture of its own, so the difference is in where you go to unwind. Frankfurt is ringed by spa towns. Wiesbaden's Art Nouveau Kaiser-Friedrich-Therme, fed by hot springs, is under an hour away, Bad Homburg has a spa park and thermal baths at the foot of the Taunus, and Bad Nauheim and Bad Soden keep up the old custom of taking the waters. In town, the Palmengarten is the main retreat from the working pace.

Luxembourg has a single spa town, Mondorf-les-Bains, half an hour away near the French border, where a mineral spring feeds pools and saunas set in a landscaped park. What the city adds is calm on the doorstep: quiet evenings and weekends, and unhurried walks through the Grund and along the Pétrusse valley without leaving the centre.