Agra or Kolkata?

Neither city has a beach or water you would swim in. The Yamuna at Agra and the Hooghly in Kolkata are rivers to look at, and in both a hotel pool is the only place to swim. The one difference is that Kolkata can reach the Bay of Bengal at Digha or Mandarmani, though at four hours or more that is an overnight trip, while Agra lies far inland on the northern plains.

Agra has its own pleasures: Mughlai kormas and kebabs, a breakfast of bedai and jalebi in the old bazaar, and boxes of petha to take home. Beyond the bazaars, though, most meals are in hotels or restaurants built for tour groups, and the city holds a curious eater for a day or two.

Kolkata is far the better place to eat, and its food is a reason to go in itself. There is hilsa in mustard sauce, prawn malai curry and sweets from old family confectioners. Add the street food, Kolkata biryani with its potato, Indo-Chinese cooking in Tangra and Anglo-Indian grills on Park Street, and there is enough variety for a whole week.

Agra has the single greater draw. The Taj Mahal, Agra Fort and Itimad-ud-Daulah make up one of the world's great groups of Mughal monuments, and they make an immediate impression even on a first visit. The catch is how narrow it is: there are few museums, and most visitors have seen it all in two days.

Kolkata's heritage is broader but harder to read. It takes in the Victoria Memorial, the imperial buildings of BBD Bagh, the Indian Museum, Tagore's family home at Jorasanko and the clay idol-makers of Kumartuli. Much of it is crumbling and takes a guide and some time to understand, and that faded grandeur is much of its appeal.

Agra has almost no nightlife. After a pre-dawn start at the Taj, evenings end with dinner and perhaps a rooftop drink facing the dome. Kolkata at least gives you somewhere to go, with Park Street's old bars and its supper-club tradition, and hotel rooftops and a few clubs in the south and Salt Lake.

Even so, a night out in Kolkata is mostly drinks and dinner, places close around midnight, and dry days shut the bars on festivals. Its great night out is Durga Puja, when the whole city tours the pandals until the small hours.

Neither city has hills or trails, but Agra has the better wildlife within easy reach. Keoladeo at Bharatpur, about an hour away, is one of Asia's finest bird wetlands in the winter months, and the Chambal sanctuary adds gharials, river dolphins and quiet boat trips.

Kolkata's green space is mostly inside the city: the lawns of the Maidan, the lakes at Rabindra Sarovar and the vast banyan at the Shibpur Botanic Garden, plus sunset boats on the Hooghly. Its great natural sight, the Sundarbans mangroves, needs two or three days rather than an afternoon.

Agra is the better base for days out. Fatehpur Sikri, Akbar's abandoned sandstone capital about 40km west, is a major sight in its own right and combines easily with Bharatpur or Deeg. The pilgrim towns of Mathura and Vrindavan are an hour north, and Gwalior's hilltop fort is two hours away by train.

Kolkata has one good day out: the string of old Danish, French, Dutch and Portuguese river towns up the Hooghly, from Serampore to Bandel. Shantiniketan, Bishnupur and Murshidabad are rewarding, but each is three hours or more away and needs a night there.

Both are hard work with children, but Kolkata gives them more to do. Science City, Alipore Zoo, the rides at Nicco Park and the Birla Planetarium fill days that in Agra would be spent only at monuments, and the Maidan gives children space to run around.

In Agra, the highlights for children are the sheer size of the Taj, the ramparts of the fort and the bear rescue centre on the Mathura road. Otherwise most families sightsee early and spend the afternoon at the pool. Even in Kolkata, the crowds and humid heat suit families who already know India.

Agra is not a city for walking. The Taj Mahal, Agra Fort, Itimad-ud-Daulah and Sikandra are spread out along and away from the Yamuna, roads are congested and pavements are broken or missing. Most visitors travel between the sights by road, in an auto-rickshaw or app taxi, or with a car and driver hired for the day. Near the Taj, polluting vehicles are kept out, so the last stretch is on foot, by electric cart or by cycle rickshaw.

Kolkata is easier to get around, mainly because of India's oldest metro, which runs north to south through the centre to Park Street and Kalighat. Cheap ferries cross the Hooghly to Howrah, and yellow taxis and autos fill the gaps, though every journey takes longer than the map suggests. Walking works mainly around BBD Bagh and the Maidan in the cooler months.

Kolkata is the better place to shop, above all for textiles. You can find Bengal handloom, Baluchari silk and kantha embroidery in Gariahat and the Dakshinapan emporia, as well as the Victorian maze of New Market and the book stalls of College Street.

Agra's speciality is narrower but distinctive: pietra dura marble inlay, still made by families of artisans, along with leather, carpets and wedding finery in Kinari Bazaar. The commission trade, in which drivers and guides steer visitors to overpriced showrooms, means shopping there takes more care.

Both are very cheap, and guesthouses, street food and rickshaws cost little in either city. The difference lies in where the money goes. In Agra the big costs are the foreigners' entry fees at the Taj and the other Mughal monuments and the luxury hotels with a view of the dome. In Kolkata entry fees are low, and the costs that add up are imported drinks and international hotel bars.

Kolkata has a real arts life. Group theatre plays most evenings at the Academy of Fine Arts and Rabindra Sadan, Tagore's songs and dance dramas are performed widely, and the Dover Lane Music Conference brings Hindustani classical music every winter. Much of the theatre is in Bengali, so visitors will usually get most out of the music and dance.

Agra's performances are mostly staged for tourists, such as shows about Shah Jahan and Mumtaz Mahal and dance evenings in the larger hotels. The spring Taj Mahotsav at Shilpgram is the one real event.

Neither is a place to unwind, and in both the reliable retreat is a hotel with a pool or spa. What differs is the quiet you can find outside it. In Agra that means the walled gardens of Itimad-ud-Daulah and Sikandra late in the afternoon. In Kolkata it means the ghats at dawn, the lawns of Belur Math and a slow afternoon of tea and adda.