The statement that accurately evaluates the impact of the flow of goods, peoples, and ideas between the Old World and the New World during the sixteenth century is:
The flow of goods, peoples, and ideas caused long-reaching societal, cultural, biological, and agricultural changes on both sides of the Atlantic.
This accurately reflects the significant and transformative effects of the Columbian Exchange, which included the movement of crops, livestock, diseases, and cultures, leading to profound changes in both regions.