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 highlights the significant and transformative effects of the Columbian Exchange, which included the exchange of crops, livestock, diseases, and cultural practices that reshaped societies in both the Old and New Worlds.