Why were the Greeks proud of their victories over the troops of the Persian kings Darius the first and Xerxes?

Why were the Greeks proud of their victories over the troops of the Persian kings Darius the first and Xerxes? which of the battles was decisive in the course of the Greco-Persian wars.

This is due to the fact that the Greeks were able to inflict a number of major defeats on the Persian troops. The most decisive was the Battle of Plataea, which took place in 479 BC. Then the main ground forces of the Persian troops were defeated, and therefore, at this stage, the hostilities were stopped, and the Greeks were able to drive the enemy out of their land.