Why is Diwali night Kali Puja in Bengal but Lakshmi Puja in Delhi?

Delhi's Lakshmi Puja and Kolkata's Kali Puja fall on Amavasya, the new moon of the same dark fortnight. The timing rules differ slightly: Lakshmi Puja looks for Amavasya in the evening, Kali Puja usually for Amavasya at midnight. Most years, those land on the same date.

Bengal already had a Lakshmi Puja, called Kojagari, on the full moon just days after Durga Puja, performed at home. So the new moon was available for something else, and a Kali worship was growing up to fill it.

The usual account credits Raja Krishnachandra of Nadia in the eighteenth century with making Kali Puja a public, patronised festival. It went on growing in the nineteenth century with wealthy Calcutta families and devotion to Sri Ramakrishna, himself a priest at the Dakshineswar Kali temple. Earlier, in the eighteenth century, the Bengali poet-devotee Ramprasad Sen wrote songs to Kali as a loving mother, and they're still sung today.

Some accounts push the origin further back, to the sixteenth-century tantric scholar Krishnananda Agamavagisha, who is said to have given Kali her familiar image. Sources disagree here, and this history needs more careful checking than a website can give it.

Lakshmi and Kali look like opposites: a calm goddess of fortune on a lotus, and a dark goddess with a garland of heads. In the Devi Mahatmya, the central Sanskrit text of goddess worship, Kali springs from Durga's brow during battle. Many devotees hold that these are faces of one Devi, and rituals in Bengal express this in their own way. Some Bengali households also worship Lakshmi on the new moon night, so the line isn't as sharp as the question suggests.

You could read the difference this way: in merchant-heavy north India, a new financial year and new account books invite Lakshmi, while in a region with a strong tantric tradition, the darkest night of the month suits Kali. It's a tempting pattern, but it's an interpretation that we can't prove, and plenty of Delhi families and Bengali families don't fit it.