Did they consider the phoenicians barbarians?
Classical Greeks considered everyone who didn't speak Greek a barbarian!
The mainland Greeks considered Phoenicians as their merchant rivals. According to a myth, the city of Thebes was founded by Phoenicians, so maybe Thebans had a more positive view of them.
The Greeks who lived in Sicily where fighting Carthage for centuries and the Carthaginians where rather cruel conquerors (of course in ancient world there where few "kind" conquerors). In 406 BC they sacked the city of Akragas (modern Agrigento), 16000 residents were slaughtered and 5000 sold as slaves.
There where certain Greek tyrants (such as Iketes of Leontinoi) that cooperated with them and used their power to prevail against their Greek enemies and many Greek mercenaries who served under the Carthaginians, but in most cases Sicilian Greeks and Carthaginians where bitter enemies.