Greece would be the furthest Persia would be able to conquer westward, with Persia only loosely exert control in Greece. And in time, become a waste and drain of resources and manpower. (A lot like Egypt was like.) Same for rebellion in the furthest regions to the East next to India. This is about Rome, but you may very well see the Achaemenids collapse on themselves in due time..
Rome may have to face with strong Hellenic states to the South in Sicily and Southern Italy. (Influx of Greeks fleeing from the East.) Rome may take in more Greek influence, or less. (The fate of Hellas.)