Dresden or Innsbruck?

Neither city is a place for beach time. Dresden's Elbe is unsafe for swimming, so on hot days it comes down to gravel-pit lakes and the ponds around Moritzburg.

Innsbruck does a little better. The small plateau lakes such as the Lanser See warm up nicely in high summer and come with mountain views, though the season is short and the big Achensee stays cold.

Both kitchens are hearty and regional rather than adventurous, and neither city is a food destination. Dresden's strengths are its baking, with Stollen and Eierschecke at afternoon coffee, wine from the Elbe valley vineyards, and a more mixed, casual spread of places in the Neustadt.

Innsbruck's best meals depend on the setting: Gröstl, dumplings and Kaiserschmarrn at a mountain hut after a climb, or strudel in an old-town coffee house. Its wine comes from elsewhere, and the tourist trap around the Golden Roof matches Dresden's around the Frauenkirche.

Here Dresden pulls well ahead. Raphael's Sistine Madonna in the Zwinger, the treasures of the Green Vault, Friedrich in the Albertinum and the rebuilt Frauenkirche form a set of world rank that needs three or four days.

Innsbruck's Habsburg heritage is smaller but compact and charming: the Golden Roof, the Hofburg, Maximilian's tomb with its bronze guardians in the Hofkirche, and Ambras Castle's cabinet of curiosities. Two or three days cover it, so for travellers who mostly come for sightseeing it works as a side dish rather than the main course.

Dresden has the livelier evenings, almost all of them in the Äußere Neustadt, where students drink in courtyard pubs and on the pavements and a few clubs occupy old industrial buildings.

Innsbruck's scene is smaller, centred on the bars set into the railway viaduct arches. In winter much of the energy moves out to après-ski in the resorts, which suits skiers but leaves the town itself quieter.

Both cities have serious landscape on hand, but Innsbruck lives inside it. The funicular and cable cars lift you from the old town to the Nordkette ridge at about 2,300m, the Karwendel opens behind it, and glaciers, ski areas, via ferratas and rafting rivers lie within easy reach.

Dresden's asset is Saxon Switzerland, a sandstone landscape of towers and gorges under an hour away by suburban train, with the Malerweg and a historic free-climbing tradition. Add the Elbe cycle route and it is excellent walking country, but it is a day trip rather than a view from your hotel window.

Both make strong bases, though they point in different directions. From Dresden the trips are about history: porcelain and the cathedral at Meissen, Moritzburg, the Königstein fortress, Leipzig, Görlitz, and Prague at the edge of a long day.

Innsbruck's rail links open up three countries: medieval Hall and glassmaking Rattenberg close by, Munich and Salzburg each a little under two hours away, and South Tyrol over the Brenner with Ötzi in Bolzano.

Both are easy, safe cities for children, with no big theme parks in either. Dresden's draws are indoor and park based: the Transport Museum, the children's section of the Hygiene Museum and the child-run miniature railway in the Großer Garten, which makes a wet day simpler to fill.

Innsbruck is better for outdoor families, with the Alpenzoo's ibex and wolves on the funicular line, adventure trails and plateau lakes in summer and ski schools in winter. Rain with small children takes more planning there.

Dresden's transport follows its river, while Innsbruck's goes straight up the mountainside. In Dresden the old town and the Neustadt are a short walk apart across the Augustus Bridge, trams cover the rest of the city, and suburban trains and paddle steamers run along the Elbe to Meissen, Pillnitz and Saxon Switzerland.

In Innsbruck the funicular leaves from the edge of the old town and links to the Nordkette cable cars, so an Alpine ridge is as easy to reach as a museum. Ski buses and valley trains cover the rest, and a car is only worth having for the remoter lakes and valleys.

Neither city is a shopping destination, and both have mainly chain-store high streets. Dresden is better for independents, with second-hand and design shops in the Neustadt, Meissen porcelain, Ore Mountain wooden toys and the Striezelmarkt in Advent.

Innsbruck's best buys are practical and traditional: excellent outdoor and ski shops, loden jackets and dirndls, Speck, schnapps and mountain cheese.

Dresden is clearly the cheaper stay. Hotels are reasonable for most of the year, eating out in the Neustadt costs little, and a day ticket covers trams and trains. Separate museum entries are the main cost that adds up.

Innsbruck carries an Alpine resort premium, most of all in ski season, and cable car tickets quickly add to the cost of an active trip. Spring and autumn are noticeably cheaper there, and the city cards that bundle lifts with transport soften the cost.

Dresden is the music city of the two by a wide margin. The Semperoper and the centuries-old Staatskapelle, the Dresden Philharmonic in the Kulturpalast and the Kreuzchor in the Kreuzkirche give a classical programme worth planning a trip around.

Innsbruck offers a solid provincial season at the Landestheater and a distinctive summer Festival of Early Music in settings such as the Spanish Hall at Ambras. It is worth checking against your dates, but it is not a draw in itself.

Dresden relaxes the way German cities do: an afternoon in the sauna of a municipal bath with cold plunges in between, a slow walk on the Elbe meadows, then cake on a terrace above the river. For a proper thermal pool, Bad Schandau is under an hour away.

Innsbruck's version is Alpine. You get mountain air, an evening at a hut, and hotel spas in Igls and the plateau villages where the sauna looks out on the peaks. The big thermal complexes of the Ötztal and Zillertal are about an hour away.