Actually the Greeks thought pretty highly of the Persians. Especially their king Cyrus had a great reputation. They were very much feared for their cavalry and admired for speaking the truth and abhorring lies. The Greeks also admired that they respected valiant warriors. For example during the Battle of Artemisium a Greek killed many Persians and was given medical care and greatly praised by the Persians. Another example, when Xerxes maltreats Leonidas's corpse after the battle of Thermopylae it is made explicit that this is extremely un-Persian behaviour. Being non-Greek the Persians were still considered barbarians of course. All of this can be found in Herodotus Histories.

I only know the Greek perspective. While Herodotus has a semi-positive view of the Persians, he was criticized in antiquity for being too nice to them - I would not take his opinion on the Persians as the norm.

Generally the Greeks viewed the Persians as slavish by birth because of their softer life (Mesopotamia is quite fertile) and by custom (living under a king). The Greeks are already quite xenophobic at best (considering anyone who didn't speak Greek a barbarian), their attitude to the state that threatened them enough to unify is probably very negative.

I'll also take a shot at your question below. There was some cultural exchange, we know Herodotus spoke to some Persians to get his anecdotes, there were embassies between Persia and Athens (it's mocked in Aristophanes), Athens and Sparta were both soliciting Persia's assistance during the Peloponnesian Wars, and Xenophon was hired as a mercenary to support a Persian prince's (unsuccessful) coup. So there was some of this at the elite level, possibly due to a culture of xenia (though I'm not sure if this practice exists among the Persians).