The vast preponderance traveled from Old World to New.
Only handfuls went to the Old World
4/5 of the people brought to the New World between 1492 and 1820 were from Africa and were enslaved
Of non-African immigrants (with the exception of New England), 4/5 were male.
Animals
Before Europeans, the only large domesticated animal in the New World was the llama
Europeans recreated their Old World lives by bringing horses, pigs, cows, sheep, and goats.
New animals had a massive effect on the flora, fauna, and landscape of the New World. It led to fencing of lands — conflicts with native peoples.
The arrival of the horse also changed the lifestyles of Pampas and Plains Indians, allowing them to survive as cohesive groups longer.
Again, direction is mainly from the Old World to New
Plants
Exchange is a little more even, but what the New World sent back had vastly greater impact
3/4s of today's crops grown for food originated in the New World.
Corn and potatoes have especially big effects on Europe and Africa spurring massive population growth — and dependency; in Ireland, a potato blight led to famine.
Cash crops (desirable commodities) in the New World sustain the exchange — tobacco, vanilla, chocolate, cotton
The Old World sent to the New rice, coffee, and sugar.
Microbes
Movement was vastly weighted in the direction of Old to New — smallpox, measles, typhus, cholera, whooping cough, plague, influenza, malaria
Pre-contact population numbers are debated but death tolls reached 80 percent in many areas.
Because of large networks of travel and exchange between native peoples throughout the Americas, disease spread to some areas in advance of settlers.