Innsbruck or Lausanne?

Neither city has a sea, so swimming means a lake in both, but in Lausanne it fits much more easily into the day. Lake Geneva runs along the whole southern edge of town, and you can swim from the lawns at Vidy or the old lido at Bellerive between other sights.

In Innsbruck you go up to the small, shallow plateau lakes such as the Lanser See, or out to the beautiful but chilly Achensee. That is a half-day outing rather than a swim on the doorstep.

Innsbruck's food is hearty mountain fuel: Gröstl, Kaspressknödel, Speck and Kaiserschmarrn, at their best in a hut after a climb. Beyond that the choice narrows quickly. There is no market life, and the wine mostly comes from elsewhere.

Lausanne eats better, mainly because of what grows around it. The Chasselas from the Lavaux terraces is poured everywhere and can be tasted from the growers in village caveaux. The Saturday market brings in the region's cheese and charcuterie, and lake perch and a strong top tier of restaurants add more range than Innsbruck can offer.

The two are well matched, but their culture comes in different forms. Innsbruck's is imperial and largely about the buildings themselves: the Golden Roof, the Hofburg, Maximilian's tomb with its ring of bronze figures in the Hofkirche, and Ambras Castle with its cabinet of curiosities.

Lausanne has one great monument, the Gothic cathedral, with a steep old town around it. Otherwise its strength is in its museums, from the Olympic Museum by the lake to the fine arts, photography and design collections at Plateforme 10.

Both cities are small university towns with more going on after dark than their size suggests, and neither is somewhere to come for the nightlife. In Innsbruck the action is in bars squeezed into the brick arches under the railway viaduct, and in winter much of the partying moves out to après-ski in the resorts.

Lausanne's equivalent is the Flon, a warehouse valley of clubs and terraces that fills on Friday and Saturday nights. In summer, evenings also spill onto the lakeside at Ouchy. The drinks cost noticeably more.

Innsbruck has the mountains right at its door. The funicular from the old town links to cable cars up the Nordkette, the Karwendel nature park lies behind the ridge, and the Stubai Glacier holds snow for most of the year. Several ski areas share one pass.

Lausanne's landscape is gentler and spread wider. Its highlights are the view of the French Alps across the lake, the walk through the Lavaux vineyards, and sailing and paddleboarding on the water. Real mountains, in the Vaud Alps or the Jura, are about an hour away rather than overhead.

From Innsbruck the trains reach three countries, but most of the big names take a while. Munich and Salzburg are each a little under two hours away, and Bolzano and Merano lie over the Brenner Pass. Neuschwanstein and the Bavarian castles need a car. Closer at hand are medieval Hall in Tirol, glassblowing Rattenberg, Kitzbühel about an hour down the line and the Crystal Worlds at Wattens.

Lausanne is the better base, because far more is close and needs no car. Vevey and Montreux are about twenty minutes along the lake, with the Château de Chillon just beyond. Geneva is under an hour and Bern only a little more, and Gruyères, Murten or a boat across to Évian fill the other days easily.

Innsbruck's family days are spent outdoors on the mountain. The Alpenzoo, with its ibex, bears and wolves, sits on the funicular line, and in summer there are adventure trails and playgrounds by the huts, with a plateau lake for a swim. A wet day is harder to fill.

Lausanne has more under a roof, with the hands-on Olympic Museum and the aquarium-vivarium, plus pedal boats and a lookout tower at Sauvabelin and paddle steamers on the lake. The trade-off is steep streets that are tiring with a pushchair, and family meals that cost a lot.

Both are easy to manage without a car, but the ground is very different. Innsbruck's centre is flat, so the old town, the Hofburg and the river are a short stroll apart, and the mountains start from a funicular at the edge of town.

Lausanne climbs steeply from the lake in layers of stairs and bridges. The m2 metro does the hard work, rising more than 300m from Ouchy to the upper town, and lake boats link the shore towns.

Neither is a shopping destination, though Lausanne has slightly more polish. Rue de Bourg is the place for Swiss watches, jewellery and chocolatiers, and the Flon adds a few small design shops.

Innsbruck's best buys are practical and local: loden jackets, dirndls, woodcarvings, Speck and schnapps. Its specialist outdoor and ski shops beat anything in Lausanne.

Innsbruck is clearly the cheaper of the two, though it still has Alpine resort prices. Spring and autumn bring hotel rates down, and the guest cards that bundle transport with lifts take the edge off an active trip.

Lausanne is expensive in every way: rooms, meals, wine and taxis. Most budget visitors end up picnicking by the lake and saving restaurant meals for one special evening, although a glass of Chasselas at a Lavaux caveau is still good value.

Lausanne has the more serious stage for its size, and dance comes first. It is home to the Béjart Ballet Lausanne and the Prix de Lausanne, and the Théâtre de Vidy produces contemporary work that tours Europe. Montreux Jazz is a short ride away in July.

Innsbruck offers a solid regional programme at the Landestheater. Its standout is the summer Festival of Early Music, held in settings such as the Spanish Hall at Ambras Castle, which is well worth timing a visit around if that is your music.

Innsbruck's way to unwind is the Alpine one: hotel spas with mountain views up in Igls, a sauna after a day on the trails, and the large thermal complexes of the Ötztal and Zillertal about an hour out. The town itself is calm and unhurried.

Lausanne has real warm springs closer by. Yverdon-les-Bains is under half an hour by train, and Lavey-les-Bains, the hottest springs in Switzerland, lies up the Rhône valley. Add the grand lakeside hotel spas and the slow walks through the Lavaux vines, and the two end up close, though Lausanne's steeper, busier centre means you find the quiet on its edges.