While Khan may have startled more butterflies and hurricanes, he did so in the manner of a natural disaster himself. He did not spread his philosophy or ideas. Or even the ideas of the Mongols. His forces were relatively small and were constantly subbing back to Mongolia. Much social change resulted. Cultures collided and many disappeared. But I cannot really see much in the way of cohesive ideology that spanned the empire beyond "submit to the khan or else."

AtG, ok the other hand, conscientiously and successfully spread Hellenism though out. He actively reshaped the societies he conquered the the extent he could. I think one of the more poignant, if not important, symbols of his cultural impact is the adoption of his hairstyle by Roman generals many years later. Or when Caesar cried to his friends after reading of his history "His friends were surprised, and asked him the reason of it. ‘Do you think,’ said he, ‘I have not just cause to weep, when I consider that Alexander at my age had conquered so many nations, and I have all this time done nothing that is memorable?"

We don't even really have a reliable description of GC's appearance.

Their impacts were different. But his cultural impact throughout the areas of his empire and beyond has and will remain identifiably Hellenistic into the foreseeable future. While the ideological legacy of the Mongols is "that of a stone dropped into water".