Alexander's success was a victory of brilliance, perseverance and great determination
I happen to agree with those that argue for Alexander's superiority over the Roman army due to his uncanny ability to find weaknesses in other armies. Over time my fascination with Alexander and the success of his expedition has only grown. As someone else said here. Persia was not a paper tiger waiting to crumble. They had huge advantages over Alexander:
1) a much bigger and better navy (Alexander was forced to take by siege all the ports in the Eastern Mediterranean, otherwise a single open port could launch seaborne attacks as soon as his army had advanced to new lands);
2) the Persian army had much better knowledge of the geography and which fields could give them advantage;
3) the Persian army already had logistical support and access to food supplies, while Alexander's army was forced to "live off the land" - this meant that Alexander had no option except to push on as quickly as he could, any failure or slow advance would exhaust his army's supplies and end his expedition;
4) the Persian army was a diversified army and one that could rely on several sorts of weapons and attacking styles, including archers, infantry, cavalry and war elephants, therefore they could have easily implemented tactics that Alexander could not;
5) Persians had the advantage of taking a leisurely walk to the battlefields and were so slow that they even brought their wives and their priests, while Alexander had to motivate an exhausted army always on the move.
Alexander’s expedition from Macedonia until India is – as far as I know – the longest military expedition in history, since several of his generals and soldiers were on a continuous military operation that lasted 9 years. These men were far from their nation and without the support of their wives (except for those they found along the way). Such a difficult expedition could only have been led by someone with an uncanny ability to always make the right decisions and the charisma to persuade everyone to give their best. I believe that the invasion of Carthage or Italy would have been much easier undertakings than what Alexander had already achieved. However, I do believe Alexander could have failed to obtain a cultural victory against Rome, in the sense that Romans would rebel and fight again in a few decades until they would win.
By the way I have created a new ancient history blog with several articles on Ancient Greece, Ancient Rome and leaders such as Alexander the Great and Constantine. You are all welcome to visit and comment on it. I called it The Million as a tribute to Marco Polo's travel and because it will collect a million historical tales:
http://themillionhistory.blogspot.cl/
themillionhistory.blogspot.cl