Baden-Baden or Cortina d'Ampezzo?

Neither town is a place for a beach. Baden-Baden is far inland on the Rhine side of the Black Forest, and Cortina is a high Alpine valley more than two hours from the Adriatic.

The swimming is different in kind, though. Around Baden-Baden, summer swimming means outdoor pools and the warmer gravel lakes of the Rhine plain. Cortina's small lakes, such as Ghedina, are beautiful to walk round but stay cold from snowmelt, so most people swim in a hotel pool.

The two eat equally well, and both serve a wealthy crowd. Baden-Baden draws on Baden's regional cooking and a French influence, but its real strength is wine: Riesling and Pinot Noir from the Rebland slopes, served in the village wine taverns. For a serious meal you drive into the northern Black Forest.

Cortina's cooking is Ampezzan mountain food with a Venetian touch, such as casunziei with poppy seeds and polenta with game. The most memorable meals are often lunches on rifugio terraces high among the peaks. In both towns the choice in the centre is narrow.

Baden-Baden has much more to see. The whole spa town is the attraction: the Kurhaus, the Trinkhalle colonnade, the villas on the hillsides, Roman bath ruins under the old town, and good art at the Museum Frieder Burda and the Staatliche Kunsthalle. That is a full day or two of sightseeing.

Cortina's centre has its basilica bell tower, painted houses and the 1956 Olympic ice stadium. The Regole museums are enough for a wet afternoon. Its most striking history is the First World War front on Lagazuoi and the Cinque Torri, and reaching it takes a day in the mountains.

Late nights are rare in both towns, and the evenings before them are spent in different ways. In Baden-Baden the night out is dressing up for the gilded casino rooms of the Kurhaus, then a hotel bar or a wine bar. The town is quiet early all year, and anyone who wants clubs goes to Karlsruhe or Strasbourg.

Cortina's evenings follow the ski season. There is après-ski when the lifts close and a passeggiata along the Corso Italia, and in the peak winter weeks a few bars and clubs stay open late. In summer the town is as quiet as Baden-Baden.

Cortina is on another level here. The Tofane, Cristallo and Cinque Torri surround the town, the Tre Cime and Lago di Misurina are under an hour away, and the same valley gives you world-class skiing in winter and hut-to-hut hiking, climbing and via ferrata in summer.

Baden-Baden's outdoors are gentler and still good. The Merkur funicular and the Battert cliffs lead into fir forest, the Panoramaweg runs through vineyards, and the Black Forest High Road climbs past the Mummelsee to the Hornisgrinde moorland. It is wooded hill country, best in autumn, with only modest skiing.

Baden-Baden is far better placed for outings. Strasbourg's cathedral and Petite France, Heidelberg and Freiburg are each about an hour away. The Alsace wine route, the Rastatt and Karlsruhe palaces, and the UNESCO sites at Speyer and Maulbronn add plenty of variety.

From Cortina, most outings go further into the mountains. The towns of South Tyrol, such as San Candido and Brunico, are the closest worthwhile trips, and Bolzano's Iceman is about two hours by road. Venice is possible, but only as a long day on the coach.

Both work for families only in certain ways, and the ways differ. Baden-Baden is safe and easy to walk, but it is built for adults, and the Friedrichsbad turns away young children. Families use it as a calm base for trips to Europa-Park and Karlsruhe's zoo.

Cortina suits families who ski or hike. It has ski schools, beginner slopes at Socrepes, skating at the ice stadium and easy walks to huts in summer. There is nothing built for children beyond that, so wet days can drag.

Baden-Baden is easier. The baths, Kurhaus and museums are a short walk apart, buses connect the centre to the station in Oos, and trains run directly to Karlsruhe, Freiburg and beyond. A car helps mainly for Alsace and the High Road.

Cortina's flat little centre is easy on foot, and ski buses work well in winter. There has been no railway since 1964, though, so arriving means a coach from Venice or a long drive. Buses up to the passes are limited, so many visitors hire a car.

Both towns are polished but narrow for shopping, each with a short upmarket strip for wealthy visitors. Baden-Baden's Sophienstraße and Lange Straße have jewellers, watchmakers and delicatessens, and cuckoo clocks and Rebland wine are the local things to take home.

Cortina's Corso Italia adds furriers and high-end mountain wear. It also has the Cooperativa di Cortina, a store dating from 1893 that sells everything from local food to outdoor gear, plus wood carving and filigree. Cortina has a little more character, and Strasbourg is the shopping trip from Baden-Baden.

Both are expensive, but Baden-Baden is easier on the budget. Its guesthouses, wine taverns and bakeries are reasonably priced for Germany, and buses are cheap. What adds up is the grand hotels and paying for each visit to the baths.

Cortina is one of Italy's most expensive resorts. Hotels and restaurants in winter and August charge luxury prices, and then come lift passes and equipment hire. Rifugio meals and the shoulder months help, but budget travellers often stay in a cheaper valley nearby.

Baden-Baden is far ahead. The Festspielhaus, one of Germany's largest opera and concert halls, brings leading orchestras and opera productions, the town's philharmonic plays in the Kurhaus, and the small nineteenth-century theatre adds drama. Brahms and Clara Schumann are part of the town's story.

Cortina has no theatre season and no regular venue. You get summer chamber music in churches and sometimes outdoors, plus a few concerts around New Year.

This is Baden-Baden's whole reason to exist. You can take the silent, unclothed circuit of hot rooms and pools at the domed Friedrichsbad, or spend a day in the indoor and outdoor pools and saunas at Caracalla, both fed by springs the Romans used. The whole town moves at the slow pace of a cure.

Cortina has no springs and no bathing tradition. Rest there comes from hotel spas with hay baths and saunas after a day on the slopes, and from quiet hut terraces in June and September. In the peak weeks it is far less calm.