Cortina d'Ampezzo or Monaco?

Cortina has no beach to speak of. It sits in a high valley more than two hours from the Adriatic, and lakes such as Ghedina and Pianozes are for walking round rather than swimming, since snowmelt keeps them cold. Most swimming happens in hotel pools.

Monaco is a real place to swim, though not a long-sand resort. Larvotto is short, sheltered and groomed, and the rest of the coast is beach clubs and rocky platforms. Cap d'Ail's coves are just over the border, and longer beaches at Menton and Nice are close by train.

Monaco is the better place to eat, mainly because it has more range. It has a striking number of starred and grand-hotel dining rooms cooking Riviera and Ligurian food, harbourside terraces, and Monégasque snacks such as barbagiuan and socca at the Condamine market. Nice and Menton are next door for cheaper meals.

Cortina's food is good mountain cooking, such as beetroot-filled casunziei, polenta with game and barley soup. Its best meals tend to be lunches on rifugio terraces high among the peaks rather than dinners in town. The valley has little street food and almost nothing international.

Monaco has more to see, all in a small area. The Rock holds the Prince's Palace and its guard ceremony, the cathedral with Grace Kelly's tomb and the Belle Époque Oceanographic Museum. Across the harbour are the Casino, the national museum's villas and the princely car collection.

Cortina's centre has the basilica with its bell tower, painted houses and the 1956 Olympic ice stadium, plus the Rimoldi art collection. Its most powerful history is the First World War front line, with tunnels on Lagazuoi and trenches at the Cinque Torri, and seeing it takes a day in the mountains rather than a stroll.

Neither is a place for casual pubs or an underground scene, but Monaco offers far more of an evening. People dress up for the Casino square, hotel bars and lounge clubs along Larvotto and the port. The principality is at its liveliest in summer and on Grand Prix weekend, and Nice is nearby for a more varied night.

Cortina's evening is après-ski drinks, a walk along the Corso Italia and a long dinner. A few smart bars and clubs stay open late only in peak winter weeks, and most summer nights are quiet early.

Cortina is one of the world's great mountain settings, and lifts take you straight from town into it. The Tofane, Cristallo and the Cinque Torri surround the valley, Lago di Misurina and the Tre Cime are within an hour, and you can ski, hike hut to hut, climb historic via ferrata routes, mountain bike or paraglide.

Monaco is built up, but its surroundings are dramatic. Old mule paths climb to Èze, the Tête de Chien cliff looks down on the principality, and coastal paths circle Cap d'Ail and Cap Martin. What Cortina cannot offer is the sea, and Monaco's clear water is good for snorkelling, diving and paddleboarding.

Monaco is the far better base for day trips. Trains run to Villefranche, Nice and Menton in well under half an hour, Èze and La Turbie are a short bus ride up the hill, and Antibes, Saint-Paul-de-Vence, Grasse, Sanremo and Dolceacqua can all be done without a car.

From Cortina, most outings go deeper into the mountains. South Tyrol has the best towns: San Candido, Brunico with its castle, and Bolzano with the Iceman, about two hours away. Venice is possible, but it is a long day by coach.

Monaco is a little easier with children over a few days. The aquarium in the Oceanographic Museum, Larvotto's sheltered water and the palace guards are all within a small, safe area, and public lifts deal with the hills. Its weak points are formal restaurants and very little else aimed at children.

Cortina works well for families who ski or hike. There are ski schools and beginner slopes at Socrepes, skating at the Olympic stadium, a forest rope park and gentle walks to huts with meadows. When the weather turns, there is almost nothing indoors for children.

Monaco is easy to get around. It is about 3km end to end, and free public lifts, escalators and a small harbour ferry deal with the steep slopes. The railway station connects the whole Riviera, so a car is more trouble than help.

Cortina's centre is flat and walkable, and in winter ski buses link it to the lifts. Beyond town it gets harder. There has been no railway since 1964, you arrive by coach from Venice or by a long drive, and buses to the passes are infrequent, so many visitors hire a car.

Both offer polished luxury shopping in a small area, and Monaco has slightly more of it. Its Carré d'Or, around the Casino gardens, gathers fashion houses, high jewellers and watchmakers, and a covered mall below adds some mainstream labels. Nice is the place for variety.

Cortina's offer is the single Corso Italia, with furriers and upmarket mountain wear. It also has two things Monaco lacks: the Cooperativa di Cortina, a department store dating from 1893, and shops selling local wood carving and filigree.

Both are among the most expensive destinations a traveller can pick, but Cortina is somewhat easier on the wallet. Rifugio lunches are fair value for their setting, and early summer and late September bring gentler rates. Lift passes and equipment hire add up in winter, however.

In Monaco cheap options barely exist, even for a coffee, and hotel rates rise further on event weekends. The free lifts and walks on the Rock help a little, but budget travellers usually sleep in Beausoleil, Menton or Nice.

Monaco is far ahead here. The Monte-Carlo Opera performs in the gilded Salle Garnier of 1879, and Les Ballets de Monte-Carlo and the Philharmonic both have international reputations. The season adds the Printemps des Arts festival, open-air shows by the sea in summer and an autumn jazz festival.

Cortina has no theatre season or regular venue. Its music comes from summer chamber and classical festivals in churches, halls and sometimes mountain settings, with the odd concert around Christmas and New Year.

In Cortina, how well you can relax depends on where you stay. There are no thermal springs or public baths, so the spa is your hotel's: a sauna, steam room and perhaps a hay bath. That is ideal after a day's skiing but leaves little for anyone in simpler lodgings. The real restorative here is the mountains themselves, such as a long lunch on a hut terrace in the clear air of June or September. August and the peak winter weeks bring crowds and traffic that undo much of that calm.

Monaco comes out ahead because it has more than hotel spas. The thalassotherapy centre next to the Casino, with warm seawater pools and treatments, is worth booking a pampering day around. Its calm is urban rather than alpine, quiet gardens and old lanes rather than empty meadows, and the mild climate makes a slow morning outdoors possible in most months. Neither place has a bathing culture you could build a whole trip around.