How barbarian, savagic nations of Europe dominanted whole world? While the east was in relatively very peaceful, the intra-warring nations of europes gained expertise at killing humans, thanks to their incessant wars of hatred with each other. East failed to keep up with developing tech to kill humans. 2nd, Western people - consisting of pirates, thieves, etc. - didn't consider humans human, and hence killed with no less ferocity as Mongols. With 1 goal: loot-maar aam shaad baad.
Source and for deeper analysis: go to Lecture # 3: 15 mins onwards i guess