Frankfurt or Lucerne?

Neither city has a sea, but Lucerne at least has a lake you can swim in right by the centre. In July and August locals swim from the old wooden lake baths, the Lido and the lawns at Ufschötti, with mountains across the water, and boats run to small bathing spots in the lakeside villages.

Frankfurt's swimming happens out of town, at gravel-pit lakes such as the Langener Waldsee, which has the sandy shore Lucerne's lawns and jetties lack. Getting there is an outing in itself, though, whereas in Lucerne you can swim between sights.

Frankfurt gives you more to eat and a stronger local character. Sitting at a shared table in a Sachsenhausen apple-wine tavern with Grüne Soße and a stoneware jug is a meal you will remember, and the Kleinmarkthalle and the cheap international kitchens of the Bahnhofsviertel add range.

Lucerne's cooking is good Swiss comfort food, with Chügelipastete, rösti and perch from the lake served in guild-house dining rooms and on terraces along the Reuss. The choice is narrow, though, prices are high, and many tables near the Chapel Bridge cater to tour groups.

The two are about level, but they offer different kinds of sightseeing. Frankfurt is a museum city: the Städel and a dozen other institutions along the Museumsufer, around a rebuilt Römer and a skyline of towers. Lucerne's appeal is the townscape itself, with the medieval Chapel Bridge, frescoed squares, the Musegg towers and the carved Lion Monument, plus Picasso and Klee at the Rosengart. Go to Frankfurt for galleries and to Lucerne for an old town that survived intact.

Frankfurt is the place for a night out. It has a serious techno and house tradition shared with Offenbach, rough-edged cocktail bars in the Bahnhofsviertel, neighbourhood bars along Berger Straße, and crowds drinking on the Main banks on summer evenings, even if the week starts quietly.

Lucerne's evenings usually end with a drink by the river, and the lakefront is nearly empty by midnight. The exception is Fasnacht, when the whole Old Town stays out in costume until dawn.

This is Lucerne's great advantage. Pilatus rises above the lake on the world's steepest cogwheel railway, Rigi offers broad ridge walks, and Titlis keeps snow all year, all reached by steamer, train and cable car. Low cloud can hide the views, but the setting is in a different league.

Frankfurt's countryside is green and gentle: the Taunus beech woods and the Großer Feldberg just north of town, the huge Stadtwald, and flat cycle paths along the Main. It is good for an easy walk or a bike ride, not for a mountain day.

Frankfurt has the deeper list of day trips, because high-speed trains put very different places within an hour or so: Heidelberg's castle, Cologne Cathedral, the Rhine Gorge with its castles and wine villages, and Würzburg's Residenz. Mainz, Wiesbaden, Speyer and Worms fill any spare days.

Lucerne reaches Zurich, Bern and Basel in under an hour and has the lake as an outing in its own right, with boats to the Rütli meadow and the William Tell country at Altdorf. The choice is good but smaller, and many of its best days out are the mountains rather than other towns.

Both work well with children, though in different ways. Frankfurt has more for a wet day, with the Senckenberg's dinosaur hall, a central zoo and the Palmengarten glasshouses. Lucerne has the Swiss Museum of Transport, which can fill a whole day, and then the journeys themselves: paddle steamers, cogwheel trains and the summer toboggan run on Pilatus. Those depend on the weather and add a lot to the cost, and with no zoo a rainy stretch can leave you short of ideas.

Lucerne is the easier of the two. The station, the steamer piers and the Old Town sit side by side on the lakefront, most sights are a flat walk along the river, and the mountain railways run on the same Swiss tickets.

Frankfurt's centre is also compact, but its U-Bahn, S-Bahn and tram network, with many lines and zones, takes more learning. In return it has an airport only a quarter of an hour from town by train and direct links to the high-speed network.

Frankfurt has more range. The Zeil handles department stores and chains, Goethestraße the luxury houses, and Berger Straße and Schweizer Straße the independent delis and design shops, with the Saturday flea market on the Main adding some character.

Lucerne is a one-subject shopping town. The watch and jewellery houses on Schwanenplatz are worth a look if a Swiss watch is on your list, alongside army knives and chocolate, but there is little for clothes or homeware.

Neither is cheap, but Frankfurt is much more manageable. Its high hotel rates come from the business trade, so weekends and summer often cost noticeably less, and tavern meals, Turkish grills and the museum pass keep daily spending moderate as long as you avoid fair weeks.

Lucerne stays expensive whatever you do. Rooms, ordinary restaurant meals and the cable cars and mountain railways that are the reason to come all cost a great deal. A Swiss travel pass and picnics by the lake soften it but do not change it.

The two are broadly level, and their calendars complement each other. Frankfurt offers depth through the season, from autumn to early summer, with an opera company known for bold productions, concerts at the Alte Oper, serious drama at the Schauspiel and jazz in cellar clubs. Lucerne peaks in late summer, just as Frankfurt goes quiet, when the Lucerne Festival brings the world's leading orchestras to Jean Nouvel's lakefront hall, though for the rest of the year its programme is that of a small town.

Frankfurt has the edge here, though the spas lie outside the city. Wiesbaden's Art Nouveau Kaiser-Friedrich-Therme and the thermal baths at Bad Homburg are both easy trips, and the old spa towns of Bad Nauheim and Bad Soden carry on the tradition of taking the waters.

Lucerne has no thermal baths of its own. Its rest comes from quiet evenings, a steamer trip with nothing to do, or the Botta-designed mineral bath high on the Rigi, while the tour-group crowds in the Old Town at midday are best avoided.