Chamonix or Strasbourg?

Neither place is a swimming destination, and the water in both is fresh water in summer only. Chamonix's swims come with mountain scenery: Lac de Passy has Mont Blanc behind it, and Lake Annecy, clear and warm, is a day's outing by car. Strasbourg's are lifeguarded gravel-pit lakes such as the Baggersee, with grassy banks, and you can reach it by tram for a hot afternoon.

Strasbourg is the better place to eat. Alsatian cooking is richer and more varied than Savoyard, with baeckeoffe, choucroute, foie gras and morning kougelhopf. The winstub, with local Riesling or Pinot Gris, gives meals a setting of their own, and there is serious fine dining in the city and the villages nearby.

Chamonix eats well on cheese: fondue, raclette and tartiflette on a terrace facing the glaciers after a day outdoors. Beyond that, the menus look much the same, and outside the main seasons a good number of kitchens close.

Strasbourg is far ahead here. The pink sandstone cathedral, the timber-framed Grande Ile, Petite France with its locks and covered bridges, and the imperial avenues of the Neustadt fill two or three days, with the Palais Rohan, the Alsatian Museum and the modern art museum by the river on top.

Chamonix's heritage is narrower but has a clear focus. It is the town where alpinism began, and the Musée Alpin, the climbers' cemetery and the statues of the first ascent tell that story well. A morning covers it.

Neither is a late-night town, but the evenings feel different. Chamonix's nights centre on winter après-ski, then a lane of pubs in the old town and a couple of small clubs, with a young, mostly English-speaking crowd of guides and seasonal workers. Strasbourg's are student bars and beer cellars in the Krutenau and around Place Saint-Étienne, then riverside terraces in summer. It is calmer, more local, and the city is mostly asleep by midnight midweek.

Chamonix is in another league here. The Mont Blanc massif rises almost 4km above the valley floor, and cable cars and the rack railway carry you straight up to hanging glaciers and granite needles. Summer brings climbing, trail running and paragliding, and winter brings off-piste skiing and ski touring.

Strasbourg's outdoors is gentler and mostly involves getting out of the city. There are flat bike routes along the Rhine with storks and beavers, then the vineyard-backed Vosges to the west and the higher Black Forest to the east, each about an hour away.

Strasbourg has more good day trips, and they are more varied. Colmar and the wine villages of the Alsace route are close by, and across the Rhine are Baden-Baden, Freiburg and Heidelberg, with Basel and Nancy also in range. Trains cover most of the cities.

Chamonix's best trips cross borders too: Courmayeur and Roman Aosta through the tunnel, Annecy and Geneva by road, and Martigny by mountain railway. After those, most places within reach are other ski resorts, and the winding roads add time.

Strasbourg is slightly easier with children, mainly because it works in any weather. It has the flat, car-free centre, boat trips, storks and rowing boats in the Orangerie, and the Le Vaisseau science centre, with Europa-Park about an hour away.

Chamonix suits outdoor families, especially with older children. The Mer de Glace train, the Merlet animal park, the summer luge and nursery ski slopes are all a hit, but the highest lifts are unsuitable for toddlers and a rainy day leaves few options.

Both are easy without a car, and Strasbourg is easier. Its walkable island centre, trams out to the station and across to Kehl, and separated cycle lanes all over the city make every journey simple. Chamonix's free valley buses and the Mont Blanc Express work well in summer, but in winter you spend a lot of time on crowded ski buses between scattered ski areas.

Chamonix is a shopping town with one subject, and that subject is equipment. If you need crampons, a harness or touring skis fitted properly, its centre is one of the best places in the Alps to buy them, and the people behind the counter know the terrain you are heading into. Beyond the gear there is little else: génépi, Reblochon, some crystals from the massif and a lot of souvenirs. Anyone after clothes or a department store drives to Geneva or Annecy.

Strasbourg is better for an ordinary afternoon of shopping, though it is no fashion destination. Place Kléber and the Grandes Arcades have the high-street names, and the lanes around the cathedral have independent bookshops and delicatessens. What you take home is Alsatian: Soufflenheim pottery, printed linens, a kougelhopf mould or a few bottles from the wine route. The December Christmas market is worth browsing carefully, as plenty of its stalls sell factory-made decorations.

Chamonix is by far the dearer of the two, and the mountains themselves are the main reason. Lift passes, the Aiguille du Midi cable car, a day with a guide or a tandem paraglide all come on top of rooms that fill at peak rates at Christmas, in the February school break and through July and August. Self-catering apartments, free buses with the guest card and trails that leave from the valley floor take some of the edge off. So does going in late spring or autumn, when it is cheaper, though some lifts stop running then.

In Strasbourg most of the bill is your hotel, because once you are there the city itself costs little. Room prices jump during the Christmas market and in the weeks when the European Parliament sits, so checking those dates before you book is the biggest saving you can make. Outside those weeks, a stay costs what you would pay in any large French regional city, well below Paris but not a bargain.

Strasbourg has a real arts calendar. The Opéra national du Rhin, the Philharmonic, the Théâtre National de Strasbourg and the autumn Musica festival of contemporary music run through the year, though you need to book around the season. Chamonix offers summer jazz, some of it played up in the mountains, and occasional church concerts and mountain film evenings. For anything more, you go to Geneva.

Both rely partly on a famous spa nearby, but the kind of relaxation differs. Chamonix's comes after effort: hot outdoor pools looking up at the glaciers after a day's skiing, and the thermal springs of Saint-Gervais in their wooded gorge, while the town itself starts early and feels busy. Strasbourg offers a slower pace, with the tiled Bains municipaux, the Friedrichsbad and Caracalla baths at Baden-Baden, and quiet canal-side walks with long winstub lunches between them.