Although in-fighting has plagued the western alliance, you are underestimating the desire of the west to be warlike, to dominate and kill as opposed to other "civilisations". Truth be told, not everyone wants to force their way of life on to others quite like the west does.
Western Europe wasnt advanced?! Rome and Greece were pretty advanced, a basic fact known by any secondary school pupil in most countries. The role of the Muslims at carrying on the elightenment of the ancient civilisations is also a factor, and the renaissance and "age of enlightenment" in Euopea is becomes a piece of the puzzle. Next stop maybe a form of multipolarity or even decline.