Florence or Lucerne?

Neither city has a beach, but Lucerne at least lets you swim on the spot. In July and August locals bathe from the Lido, the wooden lake baths and the lawns at Ufschötti, in clean, calm water with mountains behind, though the shore is grass and jetties, not sand.

Florence has nothing comparable in town, only hotel pools and public pools on the outskirts. Its proper sandy beaches are on the Versilia coast around Viareggio, warmer than the lake but a full day out by train.

Florence is a city people travel to for its food, and Lucerne is not. Florentine cooking is plain Tuscan fare done well, from rare bistecca and bread soups to lampredotto sold from kiosks, with the Mercato Centrale and Sant'Ambrogio for browsing and Chianti on the doorstep.

Lucerne serves good, hearty Swiss dishes such as Chügelipastete, rösti and perch from the lake in wood-panelled guild houses, but the range is narrow and much of the Old Town caters to coach tours. In both cities the best meals are away from the main sights, in the Oltrarno for one and the Neustadt for the other.

Florence leads by a long way here: it is one of the great art cities of Europe, while Lucerne is a handsome town with a handful of famous sights. Florence holds the core of the Italian Renaissance, from Brunelleschi's dome over the Duomo and Botticelli and Leonardo in the Uffizi to Michelangelo's David, the sculpture of the Bargello and quieter rooms such as Fra Angelico's cells at San Marco and the Brancacci Chapel. That is enough for a week of looking.

Lucerne takes a day or two. You can see the covered Chapel Bridge and Water Tower, climb the towers of the Musegg Wall, visit the Lion Monument carved into its cliff and see the Picasso and Klee of the Rosengart Collection. It is better for a stroll through the frescoed Old Town than for long days in museums.

Neither is a clubbing city, but Florence keeps going later. Aperitivo leads into wine bars, and on warm nights the crowds spill across Piazza Santo Spirito and around Sant'Ambrogio, with summer bars along the Arno and student pubs near the centre.

Lucerne is quieter still, a drink by the river and a handful of bars in the Neustadt, and the lakefront is mostly empty by midnight. The exception is Fasnacht, when the whole town parties in costume until dawn.

Lucerne's mountains and lake are the main reason to go, and Florence cannot compete. From the city you can ride the steep cogwheel railway up Pilatus, walk the ridges of Rigi, take the open-top cable car on the Stanserhorn or reach the glacier on Titlis, and steamers link it all together.

Florence has a softer, farmed landscape: olive terraces at Fiesole, the view from Piazzale Michelangelo, and cycling and walking among the vineyards of Chianti. The Casentino forests and the Apuan Alps add wilder country further out, but summer heat cuts walking short.

Florence sits in the middle of Tuscany, so the hill towns people cross the world to see are mostly an hour or so away. Siena, Pisa and walled Lucca are easy by bus or train, San Gimignano, Volterra and the Chianti villages are best by car, and the Val d'Orcia lies further south. Bologna is a quick high-speed hop to the north, and a week of outings would not repeat itself.

Lucerne has Swiss cities and the lake instead. Zurich, Bern and Basel are each under an hour by train, and steamers carry you to Brunnen, the Rütli meadow and Altdorf, where the William Tell story is set. The scenic line over the Brünig Pass to Interlaken makes a longer day, and none of it needs a car.

Lucerne is the easier place with children. The Swiss Museum of Transport can fill a whole day, the Glacier Garden and Goldau wildlife park add more, and paddle steamers, cogwheel trains and the toboggan run on Pilatus are fun in their own right. The flat, safe riverside and lakeside lawns make the pace easy, though rainy days can run short of ideas.

Florence is made for adult sightseeing. Climbing the dome, the secret passages of Palazzo Vecchio and the Boboli Gardens help, and Collodi's Pinocchio park is a good outing, but narrow pavements, summer crowds and heat make it harder going with small children.

Both centres are compact and walkable, and neither has a metro. Lucerne is the smoother of the two, since the station, boat piers and Old Town sit together on the lakefront, and the same integrated Swiss tickets carry you onto steamers, mountain railways and cable cars.

In Florence you walk almost everywhere, with trams and small buses for the airport and the hills, but narrow pavements, summer crowds and stone paving make it more tiring, and a car is useful only for the countryside.

Florence offers more, and most of it is craft. Leather from San Lorenzo stalls and small workshops, marbled paper, the goldsmiths of the Ponte Vecchio and the restorers and gilders of the Oltrarno give it real character, with luxury fashion on Via de' Tornabuoni and antiques on Via Maggio.

Lucerne is mainly about Swiss watches, sold in the large houses on Schwanenplatz, along with army knives, chocolate and cuckoo clocks. Beyond that there are a few Old Town boutiques and little fashion.

Neither city is cheap, but Florence costs far less, and you notice the gap first at the table. In Florence lunch can be lampredotto from a cart or a plate at a Mercato Centrale counter, and dinner a simple trattoria meal with house wine. In Lucerne a plain plate of rösti in an Old Town tavern costs about what a good Tuscan dinner does. Florence's big outlays are a central room in the warm months and a string of museum tickets, and both come down if you sleep across the river or come in winter.

The gap is widest once you start moving. Florence's sights are all within walking distance, and the regional trains and buses to Siena, Pisa or Lucca cost little. In Lucerne the steamers, cogwheel railways and cable cars are the reason to go, and every ride takes a real bite out of the budget. A Swiss travel pass and picnics on the lakeside lawns help, but a week in Lucerne costs a good deal more than the same week in Florence.

Both have a classical focus, and Lucerne has the edge thanks to the Lucerne Festival, which brings the world's leading orchestras to Jean Nouvel's lakefront hall, known for its acoustics, mainly in late summer. Outside festival weeks the programme is that of a small city, with the city theatre and Guggenmusik bands at Fasnacht.

Florence, where opera began around 1600, has the Teatro del Maggio Musicale Fiorentino and its long-running spring festival, but most visitors end up at concerts for tourists in churches, and theatre at the Pergola is in Italian.

The two are about level here, and neither has a bathing tradition of its own, so the difference lies in the kind of rest on offer. Florence's best relaxation is outside the city: the old spa halls of Montecatini Terme a short train ride away, the hot springs of Bagno Vignoni and Saturnia, or a few slow nights on a farm in the hills.

Lucerne is calmer in itself, with quiet evenings, lakeside promenades and long steamer rides, and Mario Botta's mineral bath on the Rigi gives you a soak with a mountain view.