Mexico City or Cancun?

This is the widest gap between the two. Cancun's Hotel Zone has around 22km of fine coral sand and warm turquoise water. The bay side has calm, shallow swimming, the eastern shore gets bigger Caribbean waves, and Playa Norte on Isla Mujeres is a short ferry ride away.

Mexico City sits on a plateau, and the Pacific at Acapulco is several hours away, so in the city swimming means a hotel pool. If you want both, plan separate days on the coast.

In Cancun, eating well means leaving the Hotel Zone, where resort buffets and international menus are rarely memorable. Downtown, around Parque de las Palapas and Mercado 28, Yucatecan cooking is the draw: cochinita pibil, sopa de lima, panuchos and fresh ceviche. Beyond that there is little range.

Mexico City is worth the trip for its food alone. Late-night al pastor, breakfast tamales from carts and counters at the Medellín and La Merced markets sit alongside the cantinas and much-praised tasting menus of Roma, Condesa and Polanco. Mezcal, pulque and Mexican-grown coffee round it out.

Cancun was built as a resort from the 1970s onwards. Apart from the Maya Museum and the small ruins of San Miguelito, El Rey and El Meco, its history lies out on the peninsula. Mexico City is the opposite: the Zócalo, the National Palace murals and the Templo Mayor stand side by side in a huge historic centre built over Tenochtitlan.

Add the National Museum of Anthropology, Chapultepec Castle, the Frida Kahlo house in Coyoacán and the canals of Xochimilco, and a week there is barely enough.

Cancun's nightlife is packed into the Party Center at the bend of the Hotel Zone: huge clubs with acrobats, confetti and open-bar wristbands that keep going until four or five. It is loud and dependable, but nearly all of it is aimed at the same vacation crowd.

Mexico City has more range and more character. A night in Roma or Condesa means walking between cocktail bars, mezcalerías and rooftop terraces, and the Centro has old cantinas. For dancing there are electronic clubs, salsa and cumbia halls, and the LGBTQ scene of the Zona Rosa.

In Cancun, the outdoors means water. You can snorkel and dive off Puerto Morelos and Isla Mujeres, see the MUSA underwater sculptures, swim in the cenotes inland, swim with whale sharks between June and September and kayak through the Nichupte mangroves. There is no real hiking.

Mexico City offers the reverse: forest walks in Desierto de los Leones and on Ajusco, with the volcanoes and the crater lakes of Nevado de Toluca about two hours away. Reaching them takes more effort, because traffic eats into the day and the air can be poor in the dry season, so Cancun's nature is the easier to enjoy.

Both cities can be a base for great pyramids, but the distances differ. From Cancun, Chichen Itza is about two and a half hours each way and Coba and Ek Balam are around two, so the big Maya sites make long days. The easy outings are Isla Mujeres by ferry and Playa del Carmen, an hour down the coast.

From Mexico City, Teotihuacan is only about an hour away, and many more towns are within a couple of hours: tiled Puebla and neighbouring Cholula, Cuernavaca, Tepoztlán and the silver town of Taxco. Leave early to beat the traffic out of the city.

Cancun is the easier family choice. Resort kids' clubs, shallow pools, the calm bay beaches at Playa Langosta and Playa Tortugas and easy first tries at snorkelling keep children busy, and the eco-parks down the coast can fill whole days. Keep an eye on the summer heat and the eastern currents.

Mexico City has more for children than its reputation suggests, from the Papalote museum and the zoo in Chapultepec to trajinera boats at Xochimilco and lucha libre. But long rides in traffic, crowded metro trains and the altitude make it harder going with young ones.

Cancun is laid out along one road. Buses along Boulevard Kukulcan to downtown are frequent and simple, but walking more than a short way is hard work in the heat on patchy pavements. Cenotes and ruins mostly mean a tour or a hire car.

Mexico City is enormous, but the districts visitors use, the Centro, Roma, Condesa, Polanco and Coyoacán, are pleasant on foot. A large metro, the Metrobús and a bike-share system link them. The downsides are rush-hour crowds and pickpockets, and ride-hailing cars fill the gaps, especially at night.

Cancun's shopping is mostly air-conditioned malls in the Hotel Zone, plus Mercado 28 downtown for souvenirs, where the same stock turns up from stall to stall. Mexico City gathers crafts from all over the country: textiles, Oaxacan pottery and alebrijes at La Ciudadela, art at the Saturday bazaar in San Ángel and antiques at the Sunday market in La Lagunilla.

It also has the luxury houses on Masaryk in Polanco and Mexican designers and bookshops in Roma and Condesa. That makes it a good choice for craft buyers and fashion shoppers alike.

Cancun's Hotel Zone is priced for international visitors. Beachfront rooms, resort meals, drinks in the Party Center and organised tours add up quickly, and an all-inclusive package makes the cost predictable rather than low. Staying downtown and eating at taco stands narrows the gap a good deal.

Mexico City is cheaper day to day. Street food, market lunches, metro rides and ride-hailing all cost little, and many museums are cheap or free on some days. Only the boutique hotels and popular restaurants of Roma, Condesa and Polanco come close to the prices of a European capital.

Cancun's shows are staged for visitors: folkloric dinner shows, resort entertainment, evening spectacles at the eco-parks and, on some nights, live music in the downtown squares. Mexico City has a real performing arts life, centred on the Palacio de Bellas Artes, home to the national opera, the symphony and the Ballet Folklórico de México.

Beyond that there are concerts at Sala Nezahualcóyotl and the Auditorio Nacional, mariachis in Plaza Garibaldi, jazz and son clubs in Roma and Coyoacán, and lucha libre at Arena México. Most theatre is in Spanish, but the ballet and the wrestling need no translation.

Cancun is the better place to slow down, because its resorts are built for it. They have large spas with hydrotherapy circuits and massages on the sand, and the Maya temazcal ritual is offered at spas and eco-retreats along the coast. The boulevard and the Party Center are noisy, so for quiet, head to the southern end of the strip, Puerto Morelos or Isla Mujeres.

Mexico City is not a restful place. It has good spas in Polanco, Roma and Condesa and its own temazcal tradition, but noise, traffic and altitude set a busier pace. For calm, try the plazas of Coyoacán, the cafés of Condesa, or a trip south to Tepoztlán.