Cortina d'Ampezzo or Venice?

Cortina's nearest sea is the Adriatic, more than two hours' drive away. Its lakes, Ghedina and Pianozes, are for walking round rather than swimming, because snowmelt keeps them cold, so swimming there usually means a hotel pool.

Venice has the only real beach of the two. The Lido is a short vaporetto ride from San Marco, with fine sand and shallow water that is warm enough for bathing in high summer. Pellestrina and the Jesolo strip are further options.

Cortina eats like a well-heeled mountain resort: casunziei with poppy seeds, polenta with game, speck and barley soup, and the best meals on rifugio terraces among the peaks. The food is satisfying but the range is narrow, with little street food and nothing cheap.

Venice offers more variety and more ways to eat. Cicchetti at bacari counters around the Rialto and in Cannaregio, lagoon seafood from the Rialto market and black cuttlefish risotto make for better grazing, as long as you avoid the picture-menu places around San Marco.

The gap here is about as wide as it gets. Cortina has a handsome bell tower, painted houses, the 1956 Olympic ice stadium and the Rimoldi collection of modern Italian art. That fills a rainy afternoon, and the First World War trenches on Lagazuoi are there for anyone willing to hike.

In Venice the city itself is the monument: San Marco, the Doge's Palace and the palazzi of the Grand Canal, then the Accademia, the Frari and San Rocco, with the Biennale in the Arsenale and Giardini. Here culture is a reason to come, not something to fall back on in bad weather.

Neither town is built for late nights, but Venice has a little more going on. Cortina's evenings revolve around après-ski and the passeggiata on the Corso Italia. A few smart bars and a club stay open late only in the peak winter weeks, and outside them the valley is quiet by late evening.

Venice's best hour is the aperitivo, with spritzes along the Fondamenta della Misericordia. Afterwards Campo Santa Margherita keeps its student bars busy a while longer, but there is no club district.

Here Cortina is far ahead. The Tofane, Cristallo and Cinque Torri ring the valley, and the Tre Cime and Lago di Misurina are under an hour away. The town reaches the Sella Ronda in winter, and in summer it has hut-to-hut hiking, climbing and paragliding.

Venice's nature is flat and watery: the salt marshes of the northern lagoon around Torcello, with herons and flamingos, seen by kayak or from a Venetian rowing boat, and cycling along the sea walls of Pellestrina. The Dolomites are more than two hours away.

Venice is the far better base for day trips. Fast trains reach Padua in about half an hour and Verona in about an hour and a quarter, with Vicenza in between. Murano, Burano and Torcello need only a boat.

From Cortina, most outings go up into the mountains. The towns within reach, such as San Candido, Brunico and Bolzano with its Iceman, are pleasant but spread out along mountain roads, and Venice itself is a long day by coach.

Both work for families, but in different ways. Cortina suits children who ski or hike, with ski schools, beginner slopes at Socrepes, public skating at the Olympic stadium and gentle trails to huts with meadows to run around in. Rainy days can drag, because there is little built for children indoors.

Venice catches young imaginations with boats instead of buses and glass-blowing on Murano, and the Lido is gentle for paddling. The stepped bridges defeat pushchairs, though, and the summer heat and crowds mean short stays with older children work best.

Cortina's centre takes only minutes to cross, and in winter lifts and ski buses serve the slopes. Beyond that a car is close to essential, because the railway closed in 1964 and buses to the passes are infrequent.

Venice is easier. Trains end at Santa Lucia, the centre is walkable and vaporetti reach the Lido and the islands. The catch is the hundreds of stepped bridges, which are hard work with luggage.

Cortina's shopping is one short street, the Corso Italia, with luxury fashion, furriers and ski wear. It is anchored by the Cooperativa di Cortina, founded in 1893, and there is some local wood carving and filigree.

Venice has more to discover: Murano glass, Burano lace, papier-mâché masks and marbled paper from working studios in Dorsoduro and Castello, with the big fashion names on Calle Larga XXII Marzo. The challenge is telling real craft from the imported copies sold along the main routes.

Both are among Italy's most expensive places to stay, and Cortina is the harder on the wallet. Hotels and restaurants charge luxury-resort rates in winter and August, and lift passes and equipment hire add more. Rifugio lunches and early-summer rates help, and many budget travellers sleep in cheaper valleys nearby.

Venice leaves a little more room to save. Eating cicchetti at a counter, staying in a quieter sestiere or in Mestre, and visiting in late autumn all bring costs down, though entry fees and water transport soon add up.

Cortina's evenings of music are mostly a summer thing: chamber and classical concerts in churches and halls, sometimes out in the mountains, with little else through the year.

Venice has La Fenice, where Verdi and Rossini premiered works, with a full season of opera, ballet and symphonic concerts, plus drama at the Teatro Goldoni and the Biennale festivals. Even a routine Vivaldi concert in a church means something in the city where he worked.

Neither place has a bathing tradition, so both rely on hotel spas, and the difference lies in the kind of calm. Cortina's Alpine spas offer saunas, hay baths and massages after the slopes. In June and September, an afternoon on a hut terrace in clear mountain air is restful in itself.

Venice's quiet comes from having no traffic, so early mornings in Castello, Cannaregio or on Giudecca are hushed. Real thermal pools are about an hour away at Abano Terme. Crowds unsettle both: Cortina in its peak weeks, and Venice around San Marco by day.