Baden-Baden or Innsbruck?

Neither town is anywhere near the sea, but Innsbruck gives swimmers a little more. The shallow Lanser See and Natterer See on the plateaus above the city warm up nicely in July and August, and the clear Achensee is beautiful to look at, though too cool for most people to swim in.

In Baden-Baden, outdoor swimming means gravel-pit lakes on the Rhine plain and public pools. Here the water you come for is the thermal kind, indoors.

The two are about level, but they suit different meals. Baden-Baden's strength is wine and a lighter touch: Riesling and Pinot Noir from the Rebland villages, Flammkuchen with a French accent from across the Rhine, and the northern Black Forest's famous restaurants a drive away.

Innsbruck's best eating is up the mountain: Gröstl, Kaspressknödel and Kaiserschmarrn at a hut after a long walk. Its wine is brought in rather than grown on the doorstep, and its student districts offer cheaper, more international food than Baden-Baden's hotel dining rooms and cake cafés.

Innsbruck has a slight edge, thanks to the depth of its Habsburg heritage. The Hofkirche, with Maximilian's tomb ringed by bronze giants, the Hofburg, the Golden Roof and Ambras Castle's early cabinet of curiosities give two or three solid days of sightseeing.

Baden-Baden's appeal is more about atmosphere than individual sights. The town itself is the exhibit: a well-preserved spa resort with the Kurhaus, the Trinkhalle and hillside villas. The Frieder Burda and Kunsthalle pair adds better modern art than anything Innsbruck shows.

Innsbruck is the livelier of the two, though neither is a party town. Its university fills the bars and small clubs in the brick arches under the railway viaduct until late at weekends, and in winter the après-ski in the surrounding resorts adds more.

Baden-Baden's evenings are formal and short. A night at the gilded Kurhaus casino, a glass in a hotel or wine bar, and quiet streets by late evening. Anyone after clubs has to go to Karlsruhe or Strasbourg.

Innsbruck is one of the few cities in Europe where high Alpine country starts at the edge of town. The Nordkette rises to about 2,300m above the old town, with the Karwendel behind it and the Stubai Glacier nearby, and you can ski, climb, raft or paraglide without much travel.

Baden-Baden has the gentler northern Black Forest: the Merkur funicular, the Battert cliffs, fir forest trails and the moorland of the Hornisgrinde. It is lovely, especially in autumn, but it is wooded upland rather than real mountains.

Both are strong bases, and Baden-Baden has slightly the richer range within easy reach. Strasbourg and the Alsace wine villages, Heidelberg, Freiburg and the UNESCO cathedral at Speyer are all about an hour away, although a car helps for the Alsace and Black Forest outings.

Innsbruck's trips go further afield. Hall in Tirol and Rattenberg are close, but Munich, Salzburg and the Bavarian castles each take around two hours. Crossing the Brenner Pass to Bolzano and Merano adds an Italian day trip that Baden-Baden cannot match.

Innsbruck is easier with children. The Alpenzoo's bears and ibex are on the funicular line, the mountain huts have playgrounds and adventure trails, the plateau lakes are warm enough for a family swim, and ski schools fill the winter.

Baden-Baden is safe and pleasant to walk around, but it is built for adults taking the waters, and the Friedrichsbad does not admit young children. Families tend to stay there and drive an hour to Europa-Park for their big days out.

Innsbruck is easier to get around. Its flat, compact centre has the main station close by, trams reach Igls and the Stubai valley, and the funicular from the old town connects to the Nordkette cable cars, so you can reach the mountains without a car.

Baden-Baden's centre is also walkable, though some streets are steep. The railway station is a bus ride out in Oos, and the High Road, the wine villages and Alsace really need a car.

Neither town is a shopping destination, but they sell different things. Baden-Baden's Sophienstraße and Lange Straße are aimed at a wealthy spa clientele, with watchmakers, jewellers, boutiques and delicatessens.

Innsbruck is more practical. It has high-street chains on Maria-Theresien-Strasse, loden jackets, dirndls and woodcarvings in the old-town arcades, and excellent outdoor and ski shops for kitting out a mountain trip.

Neither is cheap, but Baden-Baden costs more. It was built for the wealthy and still serves them, grand hotels set its prices, and every visit to the thermal baths is paid for separately.

Innsbruck charges an Alpine premium in ski season and at Christmas, and lift tickets mount up. Spring and autumn are noticeably cheaper there, and the city card bundles transport, lifts and sights.

Baden-Baden is surprisingly strong in classical music. The Festspielhaus, one of Germany's largest opera and concert houses, brings in leading international orchestras and soloists, and the legacy of Brahms and Clara Schumann still shapes the town.

Innsbruck has a sound regional programme at the Tiroler Landestheater and its symphony orchestra. Its stand-out is the summer Festival of Early Music in settings such as the Spanish Hall at Ambras, along with folk evenings and student bands that Baden-Baden lacks.

For wellness, the gap between them is wide. In Baden-Baden it is the whole point of a visit. Hot springs used by the Romans feed the domed Friedrichsbad, with its silent sequence of rooms and scrubs, and the modern Caracalla pools next door, and the rest of the town moves at the same unhurried pace.

Innsbruck has no springs of its own. Its version of wellness is a hotel sauna in Igls after a day on the trails, and the big thermal complexes in the Ötztal and Zillertal are about an hour away.