Your question is about which was the greatest empire, not the wealthiest or biggest, so I must again return to Cyrus. He was the first world leader to make education a national objective and he believed in building libraries (something Alexander the Great later copied). He incorporated the culture positivies from all the peoples beneath him and created one of the most peaceful, productive empires of all time. All of the empires you list except the Incas are defined by mighty battles and a manifest destiny type of mandate. The British are perhaps the most lucid example-- English is the most widespread language isn't it? It was not uncommon however, for tribes and peoples to rejoice when Cyrus took them into his empire (with no armed conflict at all), for his empire was far more comfortable than the ones they had previously been in.
It is interesting that History preserves the legacy of Alexander more than it does of Cyrus, but then again humility was not among Alexander's repertoire, as it was hubris that caused him to get pneumonia and drop dead in the middle of central Asia.