Cortina d'Ampezzo or Lucerne?

Neither is a beach destination, but Lucerne at least has a swimming season. In July and August locals swim from the Lido, the old wooden lake baths and the lawns at Ufschötti, and the lakeside villages you reach by boat have their own bathing spots.

Cortina's alpine lakes, Ghedina and Pianozes, are better for walking round. Snowmelt keeps them cold even in midsummer, so a swim usually means the hotel pool, and the Adriatic is more than two hours away by road.

Cortina eats better. Its Ampezzan cooking has a Venetian accent, with casunziei filled with beetroot and topped with poppy seeds, polenta with game, and barley soup. The best meals come on rifugio terraces high among the peaks, and the valley adds a few ambitious kitchens and wine bars pouring Veneto and South Tyrolean wines.

Lucerne's fondue, rösti, lake perch and Chügelipastete are reliable but rarely memorable, and many tables near the Chapel Bridge serve tour groups. Both places offer a narrow range at high prices. Cortina simply has more character on the plate.

Lucerne has much more to see. A medieval Old Town of frescoed squares, the covered Chapel Bridge and its Water Tower, the climbable Musegg towers, the Lion Monument and the Rosengart Collection make a day or two of real sightseeing.

Cortina's centre is pleasant, with the basilica's tall bell tower and the 1956 Olympic ice stadium, and the Rimoldi art collection fills a wet afternoon. Its most powerful heritage, the First World War tunnels on Lagazuoi and the Cinque Torri, takes a full day in the mountains.

Evenings end early in both towns, and Lucerne has slightly more to offer once dinner is over. Cortina's nights go from après-ski drinks to a stroll on the Corso Italia and then a long dinner. Only in the peak winter weeks do a few smart bars and a club or two stay open late, and in summer the town goes quiet early.

Lucerne has riverside wine bars, a few cocktail bars and a small club scene in the Neustadt, with students keeping it going at weekends. Its big exception is Fasnacht, the carnival before Lent, when the whole town stays out in costume until dawn.

Both have some of the finest mountain scenery in Europe, and the difference is in how you experience it. Cortina is surrounded by the pale rock towers of the Dolomites. Lifts run from town onto the Tofane and Cristallo, the Tre Cime and Lago di Misurina are under an hour away, and the terrain is serious: the Alta Via 1, historic via ferrata routes and a huge linked ski area.

Lucerne's scenery is lake and mountains together. Cogwheel trains climb Pilatus and Rigi, steamers link the shore villages, and Titlis has glacier snow all year. It is gentler and easier to reach without a car, but low cloud can hide the peaks for days.

Lucerne is far better placed. Zurich, Bern and Basel are each under an hour away by train, and Zug and Einsiedeln are closer still. The lake makes an outing in itself, with boats to the Rütli meadow and the William Tell country around Altdorf.

From Cortina, most excursions head into the mountains. South Tyrol has San Candido, Brunico and Bolzano with its Iceman, but these are charming towns rather than major sights, and Venice is a long day by coach.

Lucerne gives children more to do. The Swiss Museum of Transport fills a whole day, the Glacier Garden has its old mirror maze, the wildlife park at Goldau is close, and the steamers and cogwheel trains are adventures in themselves. The lakeside lawns are easy places to stop and play.

Cortina suits families who ski or hike, with ski schools, beginner slopes at Socrepes, public skating and a forest rope park. Beyond the outdoors there is little built for children, and with no indoor draw on Lucerne's scale, rainy days are harder.

This is one of the sharpest differences between the two. In Lucerne the station, the boat piers and the Old Town sit side by side, and trains, steamers, cogwheel railways and cable cars all run on integrated Swiss tickets, so you never need a car.

Cortina's small centre is easy on foot, and ski buses serve the slopes in winter, but the town has had no railway since 1964. Getting there means a coach from Venice or a long drive, local buses up to the passes are limited, and most visitors hire a car to explore the wider Dolomites.

Both have polished but narrow shopping aimed at wealthy visitors, and what they sell is different. Cortina's is one street, the Corso Italia, with luxury fashion, furriers, upmarket ski wear and the Cooperativa, founded in 1893, which sells everything from local food to outdoor gear.

Lucerne is mostly about Swiss watches, sold in large houses on Schwanenplatz, alongside army knives, chocolate and cuckoo clocks, with a riverside market on Saturdays. Go to Cortina for mountain fashion and to Lucerne for a watch.

Both are among the most expensive places in their countries, and you cannot do either on a tight budget. In Cortina the cost comes from peak-season hotels, lift passes and restaurants in town. Rifugio meals, early summer, late September or a room in a cheaper valley nearby can bring it down.

In Lucerne even a simple meal is pricey, and the mountain railways take a large share of the budget. Swiss travel passes and supermarket picnics by the lake help a little.

Lucerne is in another league. The Lucerne Festival brings the world's leading orchestras to Jean Nouvel's lakefront hall, which is famous for its acoustics and has its own programme all year. The Lucerne Symphony Orchestra plays there too, and the city theatre stages opera, drama and dance.

Cortina has no theatre season and no regular venue. Summer chamber music festivals play in churches and sometimes out in the mountains, and a few concerts fall around New Year, but on most evenings there is nothing on.

Neither has a tradition of thermal bathing, so both rely on hotel spas, and the setting does the rest. Cortina's spas are Alpine in style, with saunas, steam rooms and hay baths after a day on the slopes. The valley is calmest in June, September and the quieter winter weeks.

Lucerne's restful pleasures are mostly on the water: a slow steamer trip, the old wooden lake baths in summer, and Mario Botta's mineral bath on the Rigi for a soak with a mountain view. Its Old Town is crowded at midday when the tour groups arrive.