Hi there!
Alexander is perhaps the most controversial person I've ever read about. Some people love Alexander, as a cultured man who spread Greek philosophy across the world. Some people hate Alexander as a despot who had a bad temper, got very roudy when drunk, and had a short term mentality (like Victor David Hansen)
Unlike just about anyone else in history, he was both unbelievably cruel and capricious at times, killing people for no reason -- yet he was also merciful and enlightened at others (like to Darius' wife and family). Others had those characteristics, like Caesar, but Alexander's actions seem to have the least ability to be easily placed in context.
He certainly was a conqueror. After the Indus campaign, he wanted to go into the heart of India when his troops rebelled and said 'no more'.
Alexander DID go for the god bit in Egypt. When he was in Persia, he adopted the absolutism of Eastern kings, which angered his Macedonian subjects (for which kings had limited powers.). Detractors (like Hansen) believe that he got more headstrong with success. Indeed, he started adopting Persian troops. Again, people debate if he was 'inclusive', trying to be equaninimous towards his new subjects, or if he was trying to create an alternative power base from the Macedonian army.
Whether you love Alexander, hate Alexander, etc, he was an unbelievable general. I would say more of my military history brethren would put him as the greatest ever (I don't incidentally -- I put Napoleon first. But Alexander is 'up there'.)
A lot of people are taught in the US that the Greeks were these artful, peace-loving guys and that the Romans were a brawny, unimaginative military people. These are poor and inaccurate stereotypes. The Greeks were very good at war. However, they were amateurs until the 4th century BC. They could be aggressive and very warlike. Ironically, the professional and militaristic Spartans rarely went for offensive wars, while their more enlightened neighbors were aggressive.
Their innovation was bronze weapons and the hoplite tactics. Alexander's hoplites were more professional (fifth century Greek phalanxes could include very old men, blind men, etc. After all, you can't see anything in the middle of a phalanx!) and had better equipment, using a 'professional' military. His phalanx held the center. His strike force was his heavy cavalry, not his phalanxes. He personally lead the cavalry. He also introduced light troops. He was a combined arms master.
I also don't think Rome would have had troubles. If you even took the 'Greek World' as a whole in the Diodachi period, it was fearsome -- but Alexander was beginning to face revolt right when he died. I personally doubt he could have kept his empire together, and his behavior was getting more out of hand. Also, remember he was a conqueror of Greece. In the complex world, he was oppsod by the Greek governments but supported by many Greeks who joined his army.
Of course, there is speculationt hat he was poisoned. Unlike the Romans, the Macedonain conquest had a poor governmental/succession system. It was really based on the personal power of Philip and Alexander, and didn't survive their deaths (both of which may have been from assassination, or from hard living!) After his death, the difference between 'Greek' and 'Macedonian' became less important.
There is big debate about the 'Macedonian phalanx vs. the Roman legion'. The Romans fared better in real life (Pydna, Magnesia, etc.), but this was past the glory days of the phalanx. The phalanx has more straight on power -- if they met face on, the phalanx wins. But the legion is more flexible. The Romans abandoned the phalanx system during the Samnite wars since it wasn't useful in the hilly terain nearby. (Incidentally, I hear Rome: Total War does a great job of simulating this).
Anyway, aggressive is a good trait for him, as is philosphical. A fascinating man.
Best wishes,
Breunor