The principal problem of the very impressive Persian empire was, as is so often the case in empires in general, one of succession. Alexander caught them at a bad time; so, for that matter did Xenophon's Greek army earlier, who got sucked into fighting for the losing side and ended up having to cut its way to the sea.
Persia's earlier (mid-sixth-century BC) conquest of Ionia was a rather impressive show as well. A good deal of fighting, quite a great deal of diplomacy, intimidation, and bribery. Persian history that complains about Greek invasions should acknowledge that they started the thing, after all.
The fact remains that he was a military commander of amazing ability with the best army of the day.
As the chariots approached the line, the Greek soldiers in the first few rows moved sideways, forming a pocket for each chariot, with spears on all sides — the chariots were forced to stop in the pocket, and the soldiers at their rear simply killed them. The pride of the Persian Army was destroyed in minutes.
War chariots were never used in battles again.
Macedon conquering the Persian Empire would be roughly equivalent today, in manpower and other resource today to Venezuela conquering the United States.
It still seems to me the Persians had appallingly poor strategic planners. They apparently could not face the Macedonians in battle and win. So why not use Fabian tactics and attack his supply lines? With massively larger numbers, they could force Alexander to keep his army concentrated, while they still had the men to raid and attack elsewhere.
The reason this wasn’t possible is probably because the Empire was not a nation. They had to go toe to toe with the invader or lose the prestige that kept the subject nations down. The Romans and their allies had sufficient cohesion to use Fabian tactics. The Persians, not so much.