Innsbruck or Leipzig?

Neither city is anywhere near a coast, but Leipzig has the better lake swimming. Its former lignite mines have been flooded to make the Cospudener See and Markkleeberger See, which have sandy shores and beach bars and can be reached by tram or bike.

Innsbruck's swimming is in small, shallow lakes on the plateaus, such as the Lanser See, which are pleasant on a hot day, and in the Achensee, a beautiful lake that is too cold for most people. In both cities this is an afternoon out in high summer and nothing more.

The food is equally good in both, but different in character. Innsbruck's best meals are Gröstl, dumplings and Kaiserschmarrn at mountain huts, where the views do much of the work. Leipzig is more of a city for coffee and beer: it has some of Europe's oldest coffee houses and its own salty, sour Gose. Its more varied, casual eating is in the Südvorstadt and along the canals in Plagwitz, which gives it a slightly wider range than Innsbruck's old-town inns.

Both cities take two or three days to see, but the stories they tell are very different. Innsbruck's is Habsburg splendour packed into arcaded streets by the Inn: the Golden Roof, the Hofburg, and the Hofkirche, where 28 bronze figures stand around the tomb of Maximilian I. On the edge of town, Ambras Castle adds armour, Habsburg portraits and one of the earliest cabinets of curiosities.

Leipzig's history is about trade and politics. The Nikolaikirche, where the Monday prayers of 1989 began, and the former Stasi headquarters at the Runde Ecke tell the story of how East Germany ended, and Bach is buried in the Thomaskirche. The old town's covered trade-fair passages, such as the Mädlerpassage, are a sight in their own right. Further out are the three Grassi museums and the Monument to the Battle of the Nations.

Leipzig is the clear choice for going out. Its club scene grew up in empty factories and warehouses, it is built around electronic music, and weekend nights go on past dawn without strict door policies. The Karli, Connewitz and the bars in old mills in Plagwitz give you several areas to choose from.

Innsbruck's nightlife is mostly one strip of bars and small clubs in the arches under the railway viaduct, plus pubs near the university. In winter, many visitors go to après-ski in the resorts instead.

Here the two cities could hardly be more different. From Innsbruck you can reach a ridge at about 2,300m on the Nordkette in under half an hour from the old town, with the Karwendel behind it and the Stubai Glacier holding snow for most of the year. Hiking, skiing, via ferratas, paragliding and rafting all start close to the city.

Leipzig's outdoors is gentle and flat: shady paths through the Auwald floodplain forest, canoe trips along the canals, and cycling or sailing around the mine lakes. For real hills you need a two-hour train ride to Saxon Switzerland or the Harz.

Both cities are good bases, and Leipzig has the edge for the number of famous towns close by. Dresden and Weimar are about an hour away by train, Erfurt and Halle are closer still, and Wittenberg, Naumburg, Dessau's Bauhaus buildings and even Berlin are all easy to reach without a car.

Innsbruck's trips cross more borders. They include Hall in Tirol and glassblowing in Rattenberg, Munich and Salzburg about two hours away, and Bolzano and Merano over the Brenner Pass. Neuschwanstein is within reach by car.

Both cities are easy with children, but they work best for different families. Innsbruck suits families who like being outdoors: the Alpenzoo, which keeps only Alpine animals, adventure trails and playgrounds by the mountain huts, and ski schools in winter. A wet day there needs more planning.

Leipzig copes better with bad weather. Its large zoo includes Gondwanaland, a covered tropical hall, and the Belantis theme park and sandy lake shores are nearby for warm days. Once those are done, though, there is not much else aimed at children.

You can easily get around either city without a car, but in different ways. Innsbruck's flat, compact centre has an unusual extra: the funicular at the edge of the old town connects with the Nordkette cable cars, and ski buses run out to the slopes in winter. A car only helps for the remote valleys.

Leipzig adds a large tram network, an S-Bahn line under the centre, and flat streets with plenty of cycle lanes. Every day trip leaves from the same central station.

Leipzig has the slightly more interesting shopping, mostly in the west of the city: design and vintage shops and record stores on Karl-Heine-Strasse, and galleries at the Spinnerei, a former cotton mill. Its covered arcades also keep the mainstream chains dry. Innsbruck is better for things made in the region, such as loden jackets, woodcarvings, Speck and schnapps, and it has excellent outdoor and ski shops. In either city, shopping fills an afternoon rather than a trip.

Leipzig is the cheaper stay, mainly because rooms near the old town cost less than in most German cities. The exception is the big trade-fair weeks, when prices jump, so check the fair dates before booking. Elsewhere, Leipzig costs what you would expect in Germany.

Innsbruck adds an Alpine resort premium to Western European prices, which is highest in ski season and around the Christmas markets, and cable car tickets add up quickly on an active trip. Visiting in spring or autumn and buying a guest or city card makes it less expensive.

Leipzig is one of the great music cities, and the gap here is wide. The Gewandhaus Orchestra and the opera house face each other on Augustusplatz, the Thomanerchor sings Bach in his own church most weekends during term, and the city also has operetta, theatre, jazz clubs and the huge Wave-Gotik-Treffen at Whitsun.

Innsbruck has a solid regional programme at the Tiroler Landestheater and folk evenings with yodelling. Its highlight is the summer Festival of Early Music, which uses historic venues such as the Spanish Hall at Ambras. It is worth checking whether it falls during your dates.

Innsbruck is the better place to slow down. Hotels in Igls and the surrounding plateau villages have spas with mountain views, the large thermal complexes in the Ötztal and the Zillertal are about an hour away, and an evening in a mountain hut does the rest.

Leipzig's wellness is modern German sauna culture in pool complexes and a few lakeside saunas. The proper spa towns are separate trips, and its restful side is really quiet walks in the Auwald.