Cortina d'Ampezzo or Palermo?

Swimming in Cortina comes down to a hotel pool or a bracing dip in snowmelt lakes such as Ghedina, and the Adriatic is more than two hours' drive away.

Palermo is in another league. Mondello's shallow, sandy bay is about half an hour by bus and the sea stays warm from June into October, while the rocks towards Capo Gallo give deeper, quieter swimming. Neither city puts the sand at the hotel door, but only Palermo works as a beach trip at all.

Cortina eats well for a small town: Ampezzan casunziei with poppy seeds, polenta with game, and long lunches on rifugio terraces among the peaks. But the choice is narrow, almost all sit-down and rarely cheap.

Palermo is the stronger food destination by some distance. You can make a day of grazing through Ballarò and the Capo on panelle, arancine and sfincione, then try the sweet-and-sour dishes that show the city's Arab past, and finish with cannoli or brioche with granita.

Cortina's sights are pleasant rather than compelling: the basilica's tall bell tower, painted houses, the 1956 Olympic ice stadium and the Rimoldi art collection. Its most striking heritage, the First World War tunnels on Lagazuoi, is really a mountain outing.

Palermo can fill a week. The Palatine Chapel, the cathedral and San Giovanni degli Eremiti form a UNESCO-listed Arab-Norman route, Serpotta's stucco oratories add the baroque, and Palazzo Abatellis and the Salinas museum hold serious collections.

In Cortina the evening is après-ski, a stroll along the Corso Italia and a long dinner, with a few smart late bars only in the peak winter weeks. In summer the town is asleep by late evening.

Palermo has much more going on after dark, almost all of it outdoors. The Vucciria turns into a drinking spot with grills and music, the Kalsa's wine bars fill up after dinner, and on warm nights people stay out well past midnight. Proper clubs are few, though, and summer dancing moves to the beach at Mondello.

This is Cortina's great strength. The Tofane, Cristallo and Cinque Torri rise around the valley with lifts straight from town, the Tre Cime and Lago di Misurina are under an hour away, and the same slopes carry skiing in winter and via ferrata, climbing and hut hiking in summer.

Palermo's appeal is the mix of mountain and sea: the climb up Monte Pellegrino, snorkelling at Capo Gallo, the coastal trail of the Zingaro reserve and the beech woods of the Madonie. It is lovely, but smaller in scale, too hot at midday in summer and mostly needs a car.

Palermo has far richer surroundings. Monreale's mosaics are half an hour away, Cefalù is an hour by train, and Segesta, Erice and Agrigento's Valley of the Temples put some of the Mediterranean's great ancient sites within a day.

From Cortina most outings are simply more mountains. The best towns lie in South Tyrol, from San Candido to Bolzano with its Iceman, and Venice is possible but makes a long day by coach.

Cortina has a slight edge for families, but only for active ones. Ski schools, the beginner slopes at Socrepes, public skating and a forest rope park keep children busy, and the small centre is calm, though wet days drag and the costs add up.

Palermo welcomes children warmly, with late family dinners, gelato, puppet shows and Mondello's shallow bay. Daily life is harder work there: narrow lanes without pavements, uneven stone for pushchairs and heat from June to September.

Getting around is about equally easy in both, and in both places the centre is walkable and a car helps beyond it. Cortina's centre takes minutes to cross and winter ski buses link it to the lifts, but there has been no railway since 1964 and buses to the passes are sparse.

Palermo's sights line up along Via Maqueda and Corso Vittorio Emanuele, though side lanes mean dodging scooters. City buses are slow, yet regional trains do reach Cefalù and Bagheria, which gives you a few car-free outings that Cortina lacks.

The shopping is about as good in each, but very different in kind. Cortina concentrates everything on the Corso Italia: luxury fashion, jewellers, furriers, upmarket ski wear and the old Cooperativa department store. Palermo has fashion on Via Libertà, but its better finds are things to take home, such as capers and pistachio pesto from the markets, painted ceramics, handmade marionettes and the flea market near the cathedral.

Cortina is one of the costliest places to stay in Italy, with luxury-resort prices in winter and August plus lift passes and equipment hire. Rifugio meals and the shoulder months soften this only a little.

Palermo is far kinder to the wallet. A market crawl of street food makes a full meal, trattorie and local wine are cheap by northern standards, and old-centre guesthouses are fairly priced. Only seaside rooms in high summer, fish restaurants and a hire car push the bill up.

The two are not close for live performance. A winter visitor to Cortina finds little beyond a concert or two around Christmas and New Year, and an evening out there means dinner, not a show. Summer is better, when the chamber and classical festivals bring music into churches and sometimes onto the mountainsides. That makes a good end to a day of hiking, but it is a short festival season rather than a year-round programme.

In Palermo there is something to see in most months. Through the cooler part of the year the Teatro Massimo and the Politeama, a short walk apart, offer a choice of opera, ballet or an orchestral concert, and an hour at the Opera dei Pupi fits easily before a late dinner. In summer much of the programme moves into cloisters and squares. Even then, when both cities are playing outdoors, Palermo has far more on any given night.

Cortina makes it easier to unwind. Many hotels have Alpine spas with saunas and hay baths, and in June, September or quiet winter weeks the clear air and an afternoon on a hut terrace are restful in themselves.

Palermo's scooters and market noise work against rest, and wellness there means hotel spas or a train out to the thermal waters at Termini Imerese. Its calm moments are the cloisters, the Orto Botanico and the evening walk along the Foro Italico.