One historical scene in particular plays out this idea. It occurred as Cortes marched across today's Mexico towards the city and ruler he had heard so much about. At one point — not yet at the city — Moctezuma sent some emissaries to greet him. They brought two others with them, who were sacrificed in front of the Spaniards.
You can find accounts of this story from both sides: from the chronicles of Cortes and his conquistadors (Bernal Diaz, for example) and from native accounts (as told in The Broken Spears, as another example). And the differing reactions to this event tell you everything. The Spaniards were appalled, some even cried. But the emissaries were totally baffled by their reaction to the gift.
What you see is two cultures separated by an almost unimaginable amount of time, distance, and history. The clash that occurred would have been hard to prevent whenever it happened. As others have pointed out, even basic biology (immunity) was different enough to make an enormous difference without people consciously having to do anything.
Peter Watson's "The Great Divide: History and Human Nature in the Old World and the New" is a pretty fascinating examination of the overall contrasts between Eurasian and New World cultures. It's a story that's hard to tell, and there is a lot of speculation and ambiguity. What is clear, above all else, is that the whole ordeal ended tragically, insomuch as it ever ended at all.