Genghis Khan is the father of 0,2% of the world population today and killed 40 million people as he conquered. he destroyed four of the strongest nations in Asia and is responsible for the fall of the persian culture (as one of the leading nations in technology and science back then). he conquered Asia (except India, Japan and Anatolia) and managed to keep it!
Alexander fought one corrupt major power and freed the persians from the stupidity of its stupid kings (well lets face it those last kings werent as just and awesome as the founders of achaemenids were) everything else you already know probably cause of how famous that guy is!
to me gengis khan is far better than Alexander. at brutality, at diplomacy, at justice and at ruling...
only one asian king can beat Gengis khan and that is Cyrus the Great. Cyrus fought four major powers, INVENTED human rights and religious freedom. Cyrus grew to become the hero of all the ancient Greece (he was even Alexanders Hero) Cyrus didn't have a throne ready for him nor did he have a huge ass army ready for him to conquer the world with (neither did Genghis khan) while Alexander had already a throne to a country already powerful with an army trained as shit!
Alexander is extremely overrated! Cyrus is overrated amongst Persians only (since they boast about him so much) and Genghis khan has yet to become overrated :D but other famous Asian conquerors are being less talked about or discussed like Nadir Shah the last conqueror of Asia also called the Asian Napoleon since he created the same situation Napoleon Created in Europe in Asia. to most of you its not a big deal but Russian, British, French, Ottoman, Chinese, Indian and Mughal leaders all followed his actions since everyone was effected and relied on him!
i hope i answered your question but i do know that i kinda went beyond the answer! :D