Dusseldorf or Lucerne?

Neither city has a sea, but Lucerne at least has water you can swim in right in town. In July and August the Lido, the old wooden lake baths and the lawns at Ufschötti make for clean, calm swimming with mountains behind.

The Rhine at Düsseldorf looks inviting, but currents and shipping make it unsafe, so a swim means a trip out to Unterbacher See or an outdoor pool. In neither city is a swim the point of the trip. In Lucerne it simply fits more easily into a summer day.

Düsseldorf has far more to eat. There are two very different styles: the Altstadt brewhouses, serving sauerbraten, Halve Hahn and the city's sharp mustard alongside endless small glasses of Altbier, and the ramen counters, izakaya and Japanese bakeries around Immermannstrasse. Carlsplatz market adds more choice.

Lucerne serves sound Swiss cooking: Chügelipastete, fondue, rösti and lake perch in wood-panelled guild houses. But the range is narrow, many places near the Chapel Bridge cater to coach tours, and prices are high for what you get.

The two are evenly matched but quite different. Düsseldorf is a modern-art city: Klee at K20, the net slung under the dome of K21 and the broad collections of the Kunstpalast. Its bomb-damaged Altstadt is largely rebuilt, so its best historic visit is Benrath Palace out in the suburbs.

Lucerne has the old fabric that Düsseldorf lost: the Chapel Bridge and Water Tower, a well-kept medieval Old Town, the climbable Musegg towers and the Lion Monument. It has Klee too, in the Rosengart Collection alongside Picasso, but the whole city can be seen in a day or two.

Here Düsseldorf is in another league. The Altstadt's few hundred pubs and brewhouses turn weekend nights into a street party, with crowds drinking Altbier outside until well past midnight. Quieter cocktail bars in the Medienhafen and Carlstadt cover calmer evenings.

Lucerne's evenings mostly mean a drink by the water, and the lakefront is nearly empty by midnight. Both cities go wild for carnival, Düsseldorf at Rosenmontag and Lucerne at Fasnacht, but for the rest of the year only Düsseldorf offers a proper night out.

This is Lucerne's great strength. Pilatus, Rigi and the Stanserhorn rise straight above the lake, each with its own cogwheel railway or cable car, and Titlis has glacier snow all year about an hour away. Paddle steamers let you combine boat, rail and a hike in one day, and winter brings skiing.

Düsseldorf's outdoors is flat and gentle: Rhine meadows with cycle paths to Kaiserswerth, the Grafenberg forest and the wooded Neandertal. The Bergisches Land is good for a day's walk, but nothing there compares with Lucerne's mountains.

Both make excellent bases, but for different trips. From Düsseldorf the outings are towns and history: Cologne cathedral in under half an hour, the Brühl palaces, Zollverein in the Ruhr, and Aachen or Maastricht within about an hour and a half.

From Lucerne, Zurich, Bern and Basel are each under an hour by train. The lake is a day out in itself, by steamer to the Rütli meadow and the William Tell country, and the line to Interlaken crosses the Brünig Pass. The trips from Lucerne lean towards scenery, those from Düsseldorf towards cities.

Both are safe, easy cities for children, and what differs is the weather they depend on. Düsseldorf has plenty for rainy days, with the Aquazoo, the Rheinturm's tilted windows and two big theme parks, Phantasialand and Movie Park, within an hour.

Lucerne's star is the Transport Museum, which can fill a whole day. Most of its other highlights are journeys, such as steamers, cogwheel trains and the summer toboggan run on Pilatus. They are wonderful when the sky is clear, expensive, and with no zoo or aquarium to fall back on when it rains.

Lucerne is a little easier still. The station, the boat piers and the Old Town all sit together on the lakefront, and one Swiss ticket system covers buses, steamers and the mountain railways, so even big excursions start a few steps from the platform.

Düsseldorf's flat centre is just as walkable, with trams and light rail for the Medienhafen and the S-Bahn reaching the airport in minutes. Its regional network reaches Cologne and the Ruhr, though the fare zones take some working out.

Düsseldorf is the better place to shop. The Königsallee has luxury flagships and arcades along its canal, Schadowstrasse and the Kö-Bogen cover the high street, and Flingern's design shops and the Japanese quarter's stationery and homeware add something unusual.

Lucerne's shopping is mostly watches. The big houses on Schwanenplatz sit beside shops selling army knives, chocolate and cuckoo clocks for tour groups, and there is little fashion and no department store worth visiting.

Neither city is cheap, but Düsseldorf is much easier on the wallet. Its hotels are expensive for its size and soar during trade fairs, but brewhouse meals, Japanese noodle lunches and reasonable public transport keep daily spending under control.

Lucerne is expensive at every turn. Even simple meals cost a lot, and the cable cars and cogwheel railways that make the stay worthwhile are a large extra cost. A Swiss travel pass and picnics by the lake help a little, but not enough to make it a budget trip.

The two are about level, with different strengths. Lucerne has the peak: in late summer the Lucerne Festival brings the world's leading orchestras to Jean Nouvel's lakefront hall, which is famous for its acoustics. Outside the festival weeks the programme is thinner, with little live music on most nights.

Düsseldorf keeps a steadier programme all year, with opera and ballet at the Deutsche Oper am Rhein, the symphony orchestra in the domed Tonhalle, political cabaret and small jazz rooms. It is also the birthplace of Kraftwerk, though the Schauspielhaus mostly suits German speakers.

Neither city has thermal springs, and they relax in different ways. Düsseldorf has the German sauna habit, with mixed, swimwear-free saunas in its public baths, large thermal complexes within an hour and Aachen's hot springs a little further. The Nordpark's Japanese garden offers a quieter break.

In Lucerne, rest comes from the setting: an unhurried steamer trip, quiet evenings on the promenade and Mario Botta's mineral bath high on the Rigi. Each city has one loud spot to avoid, the Altstadt on weekend nights in Düsseldorf and the Old Town at midday when the tour groups arrive in Lucerne.