London or Luxembourg?

Neither city works for a beach vacation, but London at least has the coast within reach. Brighton's pebble beach is about an hour away by train, and Margate and Whitstable have sandier shores. In town there are the lidos and the Hampstead Heath ponds.

Luxembourg is landlocked, so a swim means the Upper Sûre reservoir or the Remerschen gravel pits in July and August. The lake water is actually a little warmer than the Channel, but there is no sea at all.

London is far better for eating. Its strength is the cooking of its communities, from Brick Lane curry houses to Southall's Punjabi food, Chinatown, and Caribbean and West African kitchens south of the river. Borough Market and the weekend markets in old railway arches add cheaper, casual meals.

Luxembourg is narrower: French-led restaurants, a surprisingly serious fine-dining tier and a handful of hearty local dishes. The real highlight is a glass of Moselle Riesling or crémant. Casual eating is thin, so lunch menus are where it works best.

London can keep you busy for weeks. It has several of the world's great museums, most of them free, and a thousand years of landmarks from the Tower and Westminster Abbey to Wren's St Paul's and the Georgian squares of Bloomsbury.

Luxembourg's appeal is its setting more than its collections. The UNESCO-listed fortress wraps around a sandstone plateau, the Bock casemates can be walked through and the Grund lies far below. Add the Grand Ducal Palace and MUDAM and the whole city is done well in two days.

London offers a proper night out in whichever district you pick: late bars and the gay scene in Soho, warehouse parties in Shoreditch and Dalston, big venues in Brixton. A few large clubs run until morning at weekends.

Luxembourg is smaller and runs on a different rhythm. It has a cluster of bars at the Rives de Clausen, riverside pubs in the Grund and later venues in Hollerich. Thursday and Friday are the busy nights, because many residents leave at weekends.

The two are close for green space, but it comes in different forms. London's nature is mostly inside the city: Hyde Park, Hampstead Heath's views over the skyline, and Richmond Park with its deer. The Chilterns and the South Downs are about an hour out by train and gently rolling.

Luxembourg's wooded gorges run right through the centre, and wilder country is closer. The mossy rock passages of the Müllerthal are about half an hour away, with the Ardennes hills and the Moselle cycle paths beyond.

London has the deeper list. Oxford, Cambridge and Windsor are each about an hour or less by train, and Bath, Stonehenge, Canterbury and Brighton make it easy to fill a week with very different outings.

Luxembourg's advantage is the borders. Trier's Roman gate and Metz's Gothic cathedral are under an hour away in two other countries, and Vianden's castle and the Moselle wine villages are closer still. You get variety across three cultures rather than the sheer number of choices London has.

London has far more to do with children. The dinosaur halls of the Natural History Museum, the Science Museum and the Young V&A are free, the zoo is in Regent's Park, and Legoland and the Harry Potter studio tour are close by. The downsides are long distances, Tube stairs with a buggy and crowds during school breaks.

Luxembourg is calmer and easier with a pushchair, thanks to its lifts and funicular. The casemate tunnels feel like an adventure, but apart from the Parc Merveilleux there is little made for children, so it suits a few days rather than a week.

Both are easy without a car, for opposite reasons. London has a huge network of Tube, Elizabeth line, buses and riverboats, all paid with one contactless card, but its size means long journeys, stairs and packed rush hours.

Luxembourg is small and its transport is free across the whole country, trains included. The main thing to deal with is the city's different levels, which public lifts and a funicular take care of.

London is one of the world's great shopping cities. You get luxury houses on Bond Street, bespoke tailoring on Savile Row, department stores such as Liberty and Fortnum & Mason, and weekend markets from Portobello Road's antiques to the Columbia Road flower market.

Luxembourg's Grand-Rue has premium brands for a wealthy local crowd, and little else stands out. The best things to take home are Villeroy & Boch porcelain and a few bottles of crémant.

Both are expensive, and neither will feel like a bargain. The savings come in different places. In London the national museums, the parks and many markets are free, and daily contactless caps limit transport costs.

In Luxembourg the transport is free, room rates often fall at weekends when business travel stops, and many visitors save by staying in Trier or Metz and coming in by train.

London makes its own theatre and music on a scale few cities match, while Luxembourg mostly hosts work made elsewhere. In London the West End playhouses, the National Theatre, Shakespeare's Globe and the small fringe stages above pubs sit alongside the Royal Opera House, five resident orchestras and the summer Proms at the Royal Albert Hall. Later in the evening there is jazz in Soho and rock in Camden.

Luxembourg's best night out is a concert at the Philharmonie on Kirchberg, a fine hall with its own orchestra and a steady stream of touring soloists. The Grand Théâtre, the Rotondes and the summer open-air concerts at Neimënster fill out the calendar. That gives you enough for a night or two, but not a week of different shows.

Luxembourg is the more restful choice. The thermal spa at Mondorf-les-Bains, fed by a warm mineral spring, is an easy half-hour trip, and the quiet evenings and river walks through the Pétrusse valley set a slow pace.

London has its surviving Turkish baths at Ironmonger Row and in Bayswater, hotel spas and cold dips in the Hampstead ponds. Around them the city stays fast and crowded, and proper thermal bathing means the trip to Bath.