I think what this thread comes down is not why Europe took over the world, (that's obvious, guns, steal, germs, and merchant banking) but Europe seemed to get all of those things and then thought to use them on the rest of the world to build empires that they are still benefiting from. (that or this is blatant attempt to troll the forums with thinly veiled racism) The answer to that gets down to a fundamental difference in how societies are formed and change. The best answer I've ever read to this, and which i will now try to summarize for you, comes the book "My Ishmael" by Daniel Quinn which I highly recommend reading.
Basically there are three types of land that a society can develop in. There's land where resources are plentiful, for a reasonably sized populace, then there's land where resources are too scarce, and finally there's land where resources are almost, but not quite, plentiful enough.
Africa is an example of the first kind of land, its very easy for small groups of people to live there by hunting game or gathering roots and nuts to eat. Small bands of hunter gatherers can thrive there and never really need to develop more complex systems for living, life is good there. They don't produce large technically complex societies because they don't need to. Almost all societies will only develop as far as they need to, because if were honest, humans are lazy gits and if you give any man the choice between spending six hours screwing his wife and spending six hours doing back bending labor to plow a feild which one do you think he's going to chose?
Mongolia is an example of the second type of land. Living there is very hard, to hard to be honest. People in these types of lands spend all their time just trying to meek out a meager existence and have no resource left over to invest and develop.
Europe is an example of the third, as is China, central America, the Andes Mountains, Egypt, India, and Mesopotamia. In these kinds of lands there is almost enough food. Enough food to be hungry, but not starving, to live but not thrive. To survive comfortably in these places takes effort, seeds and animals must be domesticated and once new resources are produced they must carefully managed. Managing resources requires government, which soon creates taxes and writing systems to keep track of its taxes as well as laws to maintain good order and prevent waste. Management of resource allows for investment, and experimentation, which leads to innovation, and development. Eventually such societies improve their food production to the point that they now have a surplus which can be traded or used to pay for tradesmen, such as smiths or scientist who lead to further innovation.
If a societies starts genuine food production through agriculture and resource management that society will inevitably begin to develop and create more and more complex systems. Eventually though societies settle down into a life style that is practically self supporting and comfortable, usually around 15th century technology. I.E. blossoming middle class, dwindling slave populace, early simple industrialization (mainly textiles and grain mills) under the rule of an absolute Monarch. Europe, however, is the exception to this, it never really settled down, in fact it kind of exploded around the point when is should've settled down. Why? in my opinion 2 reasons.
1st: In most areas the people who start doing all of this first gain a huge advantage over the neighbors and take over. Examples: The Han, the Assyrians, the Greeks, the Romans, the Aztecs, the Inca, and the Iroquois. They build large empires, develop to the point where their needs are satisfied and they just continue to exist until another society that went a little further comes along and takes their place.
In Europe the line of empires went like this, Assyrian, conquered by Babylonian conquered by Persians conquered by Greeks conquered by Romans conquered by Germans. But here's the kicker, the Germans were a technically inferior society to the Romans. The Roman empire was so rotted and bankrupt that they could be over whelmed by several less powerful states. This left the Germans with Roman technology (Steel and farming) in Roman infrastructure (Roads and cities) while lacking Roman superstructure (no emperor). So the Germans got to spend the next thousand years developing the absolute Monarchies to manage all their infrastructure only to then realize that now their were several different kings all more or less equal and all eyeing each other lands.
This turned Europe into a land of competition and warfare preventing them from ever feeling satisfied with their accomplishments and spurning them onward to new innovations. And it was that unending competition that eventually forced Europe to look out to the rest of the world for resources to burn on their internal conflicts.
2nd Europe is a mostly Christian area and Christianity is a weird religion. It's a Noble Aggressive religion. See Christianity draws you in with promises of how all you need to do is ask a Zombie Jew so save you from God and he will and you'll get to go to heaven when you die. Then as you spend more time studying the word of God you realize just how much of an asshole you've been to God all your life and how momentous and huge a sacrifice that Zombie Jew made to save you. And you feel really grateful to him, and so wonder if there's something you can do for him and your pastor tells that's really simply you just have to become perfect in every thought and deed. Which of course you can never actually do this side of the grave, but by that point you're all but in love with that Zombie Jew so you'll try to be perfect anyway.
The end result of which is that most Christians know that no matter what they could be better, and that they should be better. This is a powerful mindset. Give it to an engineer and the steam engine goes from being a child's toy (which is what the Greeks thought of it in the second century) to being the key to world conquest. Give it to a soldier and it become perfectly reasonable that he and his three hundred followers can conquer a city of millions. Give it to a banker and he'll start wondering what happens if he forecloses on a sub continent.
Add in to this the fact that the Zombie Jew also ordered all Christians to spend their lives convincing other people to put their faith in a Zombie Jew and you get a dangerous combination. Because priest also know that they can do better than just converting all of Europe, now they need to try to convert all the other continents too.
Ultimately what this all leads to is Jesuits insisting that even the head hunter tribes of the amazon need to be converted and the Conquistadors following them to keep them out of trouble and look for gold along the way. That's basically why Europe won.
Of course now Europe has been United into a single nation state with a unite currency and a governing body the promotes economic cooperation. And thanks to two world wars a 40 years of cold war division has heightened Europe natural pessimism and driven down church attendance in favor of a more nihilistic agnosticism. It's also technically stagnant, socially divided, and nearly bankrupt. While Christianity now finds its strongest base in the southern half of Africa where a group of technically equal peoples try to hammer out a functional government system out of tribal division and religious turmoil all while constantly eyeing each others land. So with any luck in the next three hundred years France should get colonized by the grand and glorious empire of South Africa. Which I think would be fucking awesome.