Three (modern) Americans in an ‘All-time’ list and Alexander the Great in the "might have been" list? I think you should go a litte bit deeper into strategy, and realise the value of real strategic achievments of all the above generals. The way of adapting an army to the theater needs, conducting successfull expeditionnary operations and finaly achieving strategic effects (of Alexander)over the armies he defeated AND the peoples he conquered, not only inspired allmost all of the above generals, but still constitute THE example of a superior strategy (very often failed by modern generals).
That was all very well put.
As a note on the Persians, and to help qualify Alexander’s accomplishments, it has to be said that they had been considered the best for a long time, until Alex got mardy. Their empire fitted into that category “greatest the world had ever seen” up to that point.
IMO one the best generals in history would have to be Sigismund of Poland Sigismund the Great was the man who established the PLC as one of the storngest and largest nations in Europe. He was King of Poland, HRE, and claimed the Swedesh and Russian thrones taking the later after a successful campaign. He was the man who basically gave Poland Great power status and made him one of the most strongest monarchs in the world at the time.
A great classical genera other than Alexaner would have to be Aetius Flavius. Aetius was the one who defeated the Huns and saved the roman empire from Atilla’s wrath. he was a brilliant general who accomplished amazing things given the resources he had. Why dont you recognize him. He was universally known as the last great Roman.