Why do the Persians and the Greeks react differently to the end of the Persian War

The object of the Persians was to maintain peace within their empire, which included a couple of hundred Greek city-states, which were restive, encouraged by their mother cities in mainland Greece.

The object of the Athenian-led Delian League was to prevent Persian rule of their cities.

When peace was sealed in 449 BCE, both sides agreed to stick to their own territory. This left Athens with the revenue from the League, and it spent it on beautifying its city and keeping its citizens on the public payroll, including maintaining a fleet of warships to extort the League contributions from the cities which now felt less and less like contributing to a war fund with no war but an Athens used to living off the fund.

So the Persians went about promoting stability, Athens went about imposing its will on the League, and also diverted its power to interfering in cities outside the League. To counter this, the Peloponnesian League was formed, and in due course war erupted between the two leagues for 27 years.

Persia meanwhile enjoyed the diversion of the Delian League/Athenian Empire from itself, and late in the war financed the Peloponnesian League to get rid of Athens.