Well things are very different if it's during the 1st or the 2nd medic war, because the Persian goals were very different. In the first it was mainly to punish Athens for the help it gave to the rebel cities on the coast. If defeated, Athens could either be forced to bow to the King of Kings (with the tyrant Hippias getting back his throne and a Persian garrison) or be burned in revenge for Miletus (less likely). From there either the Greeks north of Corinth are probably cowed into submission while the Peloponnese (including Corinth) fortify under the leadership (more or less forced upon them) of the Spartans while Hippias might win more influence in the North thanks to Persian support. Many of the laws of democracy are repelled and Athens never choose to become THE maritime power of its day and age, which does also give more power to the Phoenicians who can keep expanding west beyond Carthage, which may loose some independence in the long run, especially if the situation in Greece force many Greeks to flee to Sicily, reinforcing those tyrants and leading to the expulsion of the Carthaginians from the island.
If victory is achieved during the second war, then we have a much different situation because too many cities did align against Persia. In such a scenario Athens is destroyed to the ground and Thebes gets control of the north. Sparta is also destroyed and we might see an earlier Messene founded by the Persians with the freed helots as the new leading power in the Peloponnese, both Messene and Thebes being propped up by Persian subsidies and troops despite a large scale guerrilla against Persian interests in many regions. Phoenicia does not benefit from larger influence on Carthage (due to larger losses of ships) while the situation in Sicily evolves even more quickly in favor of the Greeks. The larger amount of settlers also reinforce the Greek presence in Italy (for the bad luck of the italic tribes such as the Samnites) and might relaunch colonial expansion in western Med, especially in Spain, further curtailing Carthage's ambitions. Etruscans might also loose control of Corsica (and Sardinia might as well fall to the Greeks) because they are already in their wars against Rome and on a downturn. Of course the Etruscans and Carthaginians might attempt to fight against those trend by reinforcing their alliance (cf. the Pyrgi gold tablets, which are roughly contemporary) and making a truce with Rome, Rome and the Etruscans attacking the Greeks in Campania while the Carthaginians and Etruscan fleets attempt to destroy the Greek naval forces.
I base my hypothesis on what happened after the capture of the Greek cities of Asia Minor, such as Phocea, which saw conflicts culminate with the battle of Alalia were a etrusco-carthaginian fleet was destroyed by a Greek fleet that suffered such casualties as to abandon their attempt at colonizing Corsica.