Would not the difference between Alexander and Genghis Khan be that Alexander came from a long established civilization and had culture and education. These are the benefits of culture built by
agrarian people.
Genghis Khan came from a harsh climate where people lived by hunting, not agriculture. His people were nomadic and this way of life does not encourage the development of culture. He was not much better than an animal. He would have continued to kill everyone and raze the land to return it to grazing land for his horses, if the Chinaman he carried with him, had not convinced him to leave people alone if they paid a tribute. The man from China could write, so we do have a written account of Khan's history. For sure he did not have the culture that Alexander had.
I.e. what carol said id like to highlight that again for anyone who thinks alex is greater