Innsbruck or Lucerne?

Lucerne has the better summer swimming because the lake starts at the edge of town. The Lido, the old wooden lake baths and the lawns at Ufschötti are a short walk from the centre, and the steamers stop at villages with their own bathing jetties.

In Innsbruck, swimming means leaving the city for the small plateau lakes such as the Lanser See, which warm up nicely, or the Achensee, which is beautiful but cold. Neither city has sand, and in both the season is limited to high summer.

Neither city is a food destination, but the meals feel different. Innsbruck's best eating is up in the mountains, with Gröstl, Kaspressknödel and Kaiserschmarrn at huts reached by cable car, and the student districts add some cheaper international places. Lucerne's table is set by the lake and river: perch and whitefish, the veal-filled Chügelipastete, and a glass of Swiss white on a terrace by the Reuss.

Lucerne has its Saturday riverside market, while Innsbruck has no market culture to speak of. In both cities the restaurants by the famous landmarks mainly serve tour groups.

The two are evenly matched, but their heritage is different. Innsbruck's is imperial. Its Habsburg past shows in the Hofburg, the Hofkirche with Maximilian's bronze-ringed tomb, and Ambras Castle with its cabinet of curiosities, and it takes two or three days to see properly.

Lucerne's is civic and medieval: the Chapel Bridge and Water Tower, the climbable towers of the Musegg Wall and the carved Lion Monument. The Rosengart's Picasso and Klee add modern art that Innsbruck lacks, and a day or two covers it all.

Innsbruck is the livelier of the two after dark. Its large university fills the bars and small clubs in the brick arches under the railway viaduct, which stay open late at weekends, and in winter the après-ski in the nearby resorts adds another kind of night out.

Lucerne's evenings are mostly a drink by the water and an early night, with a few cocktail bars near the station and an empty lakefront by midnight. The exception is Fasnacht, when the whole town parties in costume until dawn.

Both are outstanding mountain bases, but Innsbruck's peaks are closer and wilder. The funicular from the old town links to the Nordkette cable cars, with the vast Karwendel park behind the ridge and glaciers in the Stubai valley. Via ferratas, paragliding and rafting make it the stronger choice for active outdoor sports.

Lucerne's appeal is lake and mountains together. A day can combine a paddle steamer, the steep cogwheel railway up Pilatus and a ridge walk on Rigi, which is more of a scenic journey than an adventure, though low cloud can hide it all for days.

Lucerne is slightly the better base, because so much lies within an hour. Zurich, Bern's arcaded old town and Basel's museums are all quick train rides, and the lake itself makes a full day out, with boats to the Rütli meadow and the William Tell country around Altdorf.

Innsbruck's range is wider but its trips take longer. Hall in Tirol is ten minutes away, while Munich, Salzburg and the Italian arcades of Bolzano, home of Ötzi the Iceman, take around two hours. That gives three countries' worth of variety for those who don't mind a longer journey.

Both are safe, small and easy with children, and the difference lies in what they offer. Innsbruck's draw is outdoors: the Alpenzoo's ibex, wolves and bears on the funicular line, adventure trails and hut playgrounds in summer, and gentle ski slopes in winter.

Lucerne has the Swiss Museum of Transport, a hands-on day out that also saves a rainy day, which Innsbruck lacks. The rest is the journeys themselves, steamers, cogwheel trains and the toboggan run on Pilatus, which cost a lot over a long stay.

Lucerne is the easier of the two, as the station, the boat piers and the Old Town all sit together on the lakefront. Every excursion runs on the same integrated Swiss tickets, so boats, trains and cable cars into the mountains need no car at all.

Innsbruck's flat centre is just as walkable, and the funicular to the Nordkette leaves from the edge of the old town. Trams reach Igls and the Stubai valley, but a car helps for the remoter valleys and lakes.

Lucerne offers a little more, mainly because of its watch and jewellery houses on Schwanenplatz and the lakefront, along with army knives, chocolate and a few independent boutiques in the Old Town lanes.

Innsbruck is about Tyrolean things: loden jackets and dirndls, woodcarvings, Speck and schnapps, plus excellent specialist ski and outdoor shops. In both cities, shopping for fashion takes no more than an afternoon.

This is where the two differ most. Innsbruck is not cheap, with Alpine resort prices in ski season and around the Christmas markets, but spring and autumn bring hotel rates down, and city cards that bundle lifts and transport keep an active trip affordable.

Lucerne is in another bracket. Central hotels, simple meals and the mountain railways that make the stay worthwhile are all expensive, and supermarket picnics by the lake only soften the blow.

Lucerne is clearly ahead for classical music. The Lucerne Festival brings the world's leading orchestras to Jean Nouvel's lakefront hall in late summer, and that hall, known for its acoustics, has a year-round programme of its own.

Innsbruck has a respectable provincial programme at the Tiroler Landestheater and a distinctive niche in its summer Festival of Early Music, played in settings such as the Spanish Hall at Ambras Castle. Folk evenings with yodelling and brass add a local touch.

Neither has thermal springs of its own, and relaxing in either means hotel spas and quiet. Innsbruck's best spas are in the hotels up in Igls and on the plateaus, and the big thermal complexes of the Ötztal and Zillertal are about an hour away.

Lucerne's version is gentler and built around water: a steamer afternoon, a dip in the old wooden lake baths, or Mario Botta's mineral bath high on the Rigi. Its Old Town gets crowded at midday, while Innsbruck stays more even-paced.