Well, there's a lot to dissect in your question. People move for all sorts of reasons. Property ownership, religious freedom, adventure, or because they can. It assumes that Europe was so awful that the best option for many was to just bounce. Which might be true, but lots of people stayed. Even the ones who had the means to leave.

Still,I'm going take your assumptions seriously and suggest a big part of why living in Europe between 1492 and 1950 was awful - and it centers on war.

That's right, Europe has been the scene of nearly constant massive warfare until the gap between the Napoleonic Wars and the First World War. This displaced many people and created and destroyed many new states. But for the most part, it was a pain.

Take the Thirty Years' War which ended up with the Peace of Westphalia and, conservative estimates say, about two million casualties. Sure the result was a settlement on European religious freedom and arguably the birth of the nation-state and sovereignty. But see above, millions of dead.

There was also the War of Austrian Succession which devolved into several other conflicts even in the New World including the War of Jenkins' Ear.

Or the Dutch War in 1672 which had an estimated 500,000 casualties.

The Seven Years' War challenges my hypothesis because, it too, was fought in the New World. But the destruction wrought by the conflict killed nearly a million people. A lot of them in Europe.

And to be honest, even the so-called peace that lasted from Napoleon's last campaign to World War I was filled by Crimea, the Franco-Prussian War, and dozens of popular uprisings in central Europe.

European stability is actually a really new and novel thing. If there wasn't a Great Power War, there was some local conflict that picked up the slack. Why that is should be addressed another day. But if there is a reason why people would leave Europe for the New World, it's the same reason lots of people still come to America today - the local situation is fraught and unstable.