I can't really give an answer to that question, but I'll give some facts.
Macedonian Army
The army that invaded Persia in 334 BC consisted of following units:
Pezhetairoi (9,000)
Hypaspists (3,000)
Greek ally hoplites (7,000)
Allies, including Cretan archers
Balkan warrirors, including Thracians, Illyrians, Agrians, Triballians and even Celts (6,000), serving as light troops
Hetairoi cavalry (1,200)
Prodromoi (scouts) (600)
Thessalian cavalry (1,200)
Greek ally cavalry (1,000)
Mercenary cavalry (600)
Thracian and Paionian cavalry (900)
Pioneers and siege engineers.
A small who's who:
Pezhetairoi:
Classic phalanx. Renamed into
pezhetairoi by the Macedonians, meaning as much as "infantry companions". Theiy carried 5m long lances, so-called
sarissa, and marched in phalanxed formation, each man almost touching the next one by the shoulder. They carried heavy armour for protection.
Hypaspists:
Light infantry, actually "royal shieldbearers". An elite corps, meant for quick attack, aka as the "best infantry of antiquity". They carried lances, swords and shields.
Greek allies:
Classic hoplites. Armed similarly to the pezhetairoi, but not in a heavy phalanx formation and shorter sarissa, but carrying shields. They were not to be trusted, and thus not used offensively.
Cretans, allies and mercenaries:
The Cretans were best archers of the Greek world, meaning nothing. The Greeks weren't very keen archers. But, like all allies and mercenaries, keen on battle. Thracians, Thessalians, Illyrians, Celts etc. were great warriors, but in inferior numbers.
Hetairoi:
Macedonian knights, if you want it that way. Heavily armed horsemen. Armed with short lances and sabre. Armoured with helmets, leather armour and all that fancy stuff.
The elite cavalry, even superiour to the regular Persian cavalry.
Prodromoi:
Scouts, on fast horses. Moved fast on the excellent Persian road network, but no value in combat.
Thessalians:
The strongest and best cavalrymen south of Macedonia, again, meaning little. The Greeks weren't that keen of horsemanship until Philipp of Macedon introduced the cavalry to regular Macedonian warfare. Since these were more of Greek allies, they weren't to be trusted either.
The Macedonians faced an army which consisted of fierce warriors, but wasn't very effective against the Greek "art" of war. The oriental army was ligthly armoured, and didn't rely that much on infantry. Iranian archers and slingers were indeed the most skilled of this part of the world at that time, but their impact on the heavily armoured Greek infantry was close to zero.
The Persians relied more heavily on cavalry. The backbone of the cavalry consisted of mounted archers, scythed chariots and cameleers. Elephants were also used, but not so extensively.
Alexander was at best a moderate strategist, but an able commander and an excellent leader. He wasn't much of a general, but he knew how to motivate his troops. In his battles against Persia, he had more able generals and commanders at his side: Parmenion and Krateros most of all.
The Persian army was not as organized. At the battle at the Granicus, it was a mere satrapal force, as was used in the preceeding two centuries to fight revolts and occasional invaders. The troops were well-trained, but light at best, and consisted mostly of mercenaries.
At Issus and Gaugamela, the Persians used their "imperial body", an army consisting of conscripts, mercenaries and other troops from all over the empire. Such armies were previously used by Darius the Great (522-486 BC) in 512 BC, against Scythia, and 490 BC, against Athens, by Xerxes I (486-465 BC) against Athens in 480 BC, and propably again in 466/65 BC, and by Artaxerxes II (404-359 BC) against his revolting brother, Cyrus, in 401 BC; though it is likely that similar bodies were used to fight other serious revolts.
Darius III (336-330 BC) lead the army himself, which was propably intended as a moral boost for the troops, but ended in disaster. The death or flight of the commander automatically meant the loss of the battle for the Persians, as in 479 BC, or 401 BC (death of Cyrus). Had Alexander not chased for Darius, the Persians might have won the battles of Issus and Gaugamela, due to the massive use of heavy cavalry, and the sheer number of soldiers (Greek sources claim that the Persian troops were about 1 million at the battle of Gaugamela, but they were more likely to be about 240,000, which is still a huge number).
A quick word on the Macedonian battle tactic: Philipp of Macedon introduced the Theban tactic, courtesy of Epameinodas, to his army. Epameinodas changed the standart Greek tactic, of frontal clash between two equal phalanges by adding a corps which was supposed to encircle the enemy. This could be an extra phalanx, or cavalry (Epameinodas used infantry, the Macedonians used cavalry). Of course, this didn't quite work with the huge Persian army, so Alexander decided to attack the centre of the Persian army with his cavalry, in order to chase away the Great King, while his infantry fought off the Persian cavalry. Alexander took the risk of the Persians encircling him (at Gaugamela, they even started looting his camp), because he knew that the Persians wouldn't keep fighting without their commander.
After the conquest of Persia itself (which was, in fact, not more than the region around Persepolis, Pasargadae, Seraz (Shiraz) and Tauka), and central Iran, Alexander was forced to change tactics. Macedonian troops were defeated by the Sakan tribes of central Asia, who were fierce horsemen, and made no prisoners. In the mountain war against Spitamenes and his successors, the Macedonian troops replaced their sarissa by simple short swords. The effect wasn't staggering, but it was, in the end successful. By the time the Macedonians reached India, the Macedonian troops were weary, tired, wounded and reduced, although Iranian conscripts, trained in Macedonian way, kept reinforcing; these were also the ones to die first.
The battle against Porus was very, very bloody, and it is even doubted that the Macedonians actually won; the positive result is propably the effect of diplomacy.
This was a short military rundown (by a pacifist) of the Macedonian army under Alexander. Sources were Hans-Joachim Gerhke, "Alexander der Grosse", S. Fischer-Fabian, "Der Traum vom Frieden der Völker, Alexander der Grosse", and my own memory. [advert] For further information on Alexander and the Persians, I'd like to invite German speakers to visit my site at:
http://www.alexanderthegreat.de[/advert]
My knowledge about the Roman army is not as comprehensive (though I do not dare to call my knowledge on the Macedonian/Greek army "comprehensive", but this is a comparisson). It'd be interesting to see a similar rundown on Caesar's army at such battlesites as Alesia or Pharsalos.