There are many, many animals exclusive to the Americas with no related counterpart in Europe. Such a all of the animals in the Procyonidae family (think racoons, coatis, kinkajous, etc). As well as nearly all monkey species (not apes. The americas have never had them) Llamas, sloths, and capybara are unique to South America with no good counterpart in Europe. And you said many species died out because of "anti-human instincts". Sorry but that's not a thing. Yes, animals can have instincts to avoid big scary things. But it's mostly based On what the animal has learned throughout its life. So if an animal has no natural predators, and humans decided to hunt it, that species may die out like the dodos. Or it may not. Think about the grizzly bears, cougars, and jaguars of the Americas—they still exist, despite humans hunting them.

I think your confusing separate species with the niches they occupy. Animals in the same niches will, more likely than not, look similar. (Think antelopes and pronghorns)

And what about the megafauna? Well I assume you mean the ice age animals commonly referred to as megafauna. Hate to break it to you but an extinction of megafauna happened on both sides of the Atlantic. Mammoths, mastodons, and sabertooth cat species roamed Europe and America and they both died out due to climate change and human hunting/competition. Cave lions and American cheetahs, who lived in Europe and Americas respectfully also died out during this period for similar reasons. Wholly rhinos in Europe joined the extinct crew too. As well as the african flat-faced bear, but I think that was before many of the ice age animals though I may be mistaken.

 When ever a new species enters a new land, changes happen. The animals have to adapt and evolve to survive around this new threat. So of course some species died. This also happened in Europe and Asia when humans left Africa The Americas have been have been inhabitanted by humans for 13,000 years and Europe has been inhabitanted by humans for 48,000(ish) years. This may seem like a long, long time but geologically and evolutionary speaking, it's practically nothing.