The Greeks of this time period were not united under kings. They were all city states. Of course, some cities had kings, but the Greek world was fragmented. In fact, too often the Greek would even fight each other and I would argue that was one of their greatest weaknesses. Persia, on the other hand, had a huge empire. They were united under the Great King. And the two people even went to war many times, until the Greek under Alexander defeated them.
Also, if we compare the Athenians to the Persians. The Athenians had a democratic government, which was was pretty much the opposite of Perisa.
A few more things. They had different languages, religions and cultural expressions.