Dowries exist in societies where capital is more valuable than manual labor. For instance, in Middle Ages Europe, the family of a bride-to-be was compelled to offer a dowry — land, cattle and money — to the family of the husband-to-be.[citation needed]
Bridewealth exists in societies where manual labor is more important than capital. In Sub-Saharan Africa where land was abundant and there were few or no domesticated animals, manual labor was more valuable than capital, and therefore bridewealth dominated. In Eastern Europe, the bride’s family is compensated for their loss of a worker.[citation needed]
An evolutionary psychology explanation for dowry and bride price is that bride price is common in polygynous societies which have a relative scarcity of available women. In monogamous societies where women have little personal wealth, dowry is instead common since there is a relative scarcity of wealthy men who can choose from many potential women when marrying.[4]
Dowry comes from the bride’s side, bride price comes from the groom’s.
What historical conditions resulted in money flowing one way vs the other?
I didn’t know, so I googled it - wiki says