Innsbruck or Strasbourg?

Neither city has a sea, so swimming in both means a summer afternoon at a lake. Innsbruck has a slight edge for setting. The Lanser See and Natterer See on the plateaus above town warm to about 22°C in high summer and come with peaks behind them, while the Achensee further out is lovely to look at but cold to swim in.

Strasbourg's lakes are old gravel pits on a flat plain. The Baggersee is a tram ride away and has grassy banks and lifeguards in July and August. They are practical rather than scenic, and the Rhine itself is off limits.

Strasbourg is clearly the stronger place to eat. Alsatian cooking is richer and more varied, from tarte flambée and baeckeoffe to foie gras, and the winstub tradition pairs it with Riesling, Sylvaner and Pinot Gris grown a short way south. Add a covered market for Munster and charcuterie, a serious fine-dining tier and plenty of local beer.

Innsbruck's Tyrolean food of Gröstl, Kaspressknödel and Kaiserschmarrn is filling and honest, and is at its best in a mountain hut after a hike. In town the choice narrows quickly, with no market culture, wine brought in from elsewhere and tour-group menus around the Golden Roof. Both cities have the same weakness around their famous squares.

Both cities cover their main sights in two or three days, but Strasbourg packs more into that time. The pink sandstone cathedral with its astronomical clock, the timber-framed lanes of Petite France and the German-built Neustadt form one UNESCO-listed whole. The Palais Rohan alone holds three museums, and a large modern art museum and the European institutions add a twentieth-century side.

Innsbruck's heritage is Habsburg and compact: the Golden Roof, the Hofburg and above all the Hofkirche, with Maximilian I's tomb and its ring of bronze giants. Ambras Castle's cabinet of curiosities is a real treat, but the museum list ends sooner.

Evenings out are modest in both, each kept going by a big university, but the feel differs. Innsbruck has its strip of bars and small clubs in the brick arches under the railway viaduct, which stays open late at weekends, and in winter much of the partying moves out to après-ski in the resorts.

Strasbourg is more about bars than dancing. Student pubs and beer cellars fill Krutenau and Place Saint-Étienne, and summer terraces along the quays stay busy into the evening. With only a handful of clubs, the city is mostly asleep by midnight on weeknights.

This is where Innsbruck pulls furthest ahead. High Alpine terrain starts at the city's edge: the Nordkette ridge at about 2,300m is under half an hour from the old town, the Karwendel nature park lies behind it, and the Stubai Glacier keeps snow for most of the year. Skiing, via ferratas, paragliding and rafting are all close by.

Strasbourg is flat and green, with storks and beavers in the Rhine forests and long level cycle routes into Germany. Its real hills, the Vosges and the Black Forest, are about an hour away and easier to reach with a car.

Both make good bases, but Strasbourg's trips are closer together and easier to string along. Colmar is half an hour south by train, the wine route villages of Riquewihr and Eguisheim sit between the two with Haut-Koenigsbourg above them, and across the Rhine are Baden-Baden, Freiburg and, a little further, Heidelberg.

Innsbruck reaches three countries from its spot on the Alpine rail lines. Hall in Tirol and glassblowing Rattenberg are near, but the big names, such as Munich, Salzburg, Bolzano with Ötzi, and Neuschwanstein by car, each take close to two hours.

Families do roughly as well in either, in different ways. Innsbruck's appeal is the mountains: the Alpenzoo with its ibex and lynx on the funicular route, adventure trails and hut playgrounds in summer, and ski schools on gentle slopes in winter. The catch is wet weather, when there is little indoors built for children.

Strasbourg copes better with rain, thanks to the hands-on Le Vaisseau science centre, boat trips round the Grande Ile and the clock's moving figures. The Orangerie has storks and rowing boats, and Europa-Park, one of Europe's biggest theme parks, is an hour across the border.

Both have small, flat centres you cross on foot, and neither needs a car. What sets Innsbruck apart is how easily public transport reaches the heights, with the Hungerburg funicular, trams to Igls and the Stubai valley, and ski buses in winter.

Strasbourg's strength is the bike. Separated lanes and bike hire make cycling the quickest way round, and the trams run out to the European quarter and over the Rhine to Kehl. In both, a car only pays off for remote valleys or the wine villages.

Strasbourg gives shoppers more to do. Around Place Kléber and the Rue des Grandes Arcades there are chains and a department store, and the lanes by the cathedral hold bookshops, delicatessens and independents. Soufflenheim pottery, printed linens and kougelhopf moulds make good souvenirs, and December brings the long-running Christmas market.

Innsbruck's Maria-Theresien-Strasse is mostly chains, but the city wins outright on one thing: specialist outdoor and ski shops. Loden jackets, dirndls, Speck and schnapps are the local buys.

Neither is cheap, but Strasbourg is a little gentler on the budget. Winstub meals and tarte flambée are fairly priced, wine by the pichet is good value, and the cathedral and old town streets cost nothing. Hotels are the main expense, and they spike during the Christmas market and when the European Parliament sits.

Innsbruck carries an Alpine resort premium, and cable car tickets add up fast on an active trip. Guest cards that bundle lifts and transport soften the blow, and spring and autumn are clearly cheaper than the ski season.

Strasbourg has the fuller programme. The Opéra national du Rhin on Place Broglie, a philharmonic with a complete season and the Théâtre National de Strasbourg, one of France's leading stages, are backed by the Musica contemporary music festival in autumn and a well-regarded jazz festival.

Innsbruck's Landestheater and symphony orchestra make a sound provincial offering, and the summer Festival of Early Music in Ambras Castle's Spanish Hall is a real highlight. It also has something Strasbourg lacks: folk evenings with yodelling and brass bands.

Strasbourg is the better place for a proper soak. Its early twentieth-century Bains municipaux has tiled pools, a hammam and saunas in town, and Baden-Baden's Friedrichsbad and Caracalla baths are under an hour away. Canal-side walks and long winstub lunches keep the pace slow, though not in December.

Innsbruck has no thermal water of its own. Relaxing there means mountain air and hotel spas in Igls and the plateau villages, often with saunas looking onto the peaks, while the big thermal complexes in the Ötztal and Zillertal are about an hour out.