As I wrote elsewhere, I think the aims between Caesar and Alexander were different, but each wanted to use his talents to the utmost level possible - and neither, in other times and places, would have had the chance. I remember a wonderful story I read aeons ago (by Stephen Vincent Benet, of all people!) about an 18th-century Englishman visiting this small resort in France, where he tumbled upon an unusual elderly Frenchman (married to a Creole), both living on a limited income; the Frenchman was quite fascinating (actually, he was born in one of France's Mediterranean possessions) because he seemed so very good, as a hobby, at discussing war and strategy. And of course, at the VERY end of the story (with little prefiguring) you find that his name is Napoleone Buonoparte, and that he was a middling Corsican civil servant who would be dead 30 years before the wars leading into the French Revolution.

I think Caesar and Alexander's talents would have shown in any possible context, but the fact that each lived in times which threw opportunities in their way - and that they both took them and ran with them almost beyond the limits of the possible - is also vital. The gods willed it?