I just watched 300: Rise of an Empire, and there is a clear emphasis on the rowers used in the opposing fleets. The Persians use chained slaves while the Greeks use free citizens. Is this depiction accurate to the time period, or did both sides use galley slaves as rowers?
It is indeed inaccurate, but the other way around. Neither side used galley slaves.
Galley slaves did exist, and fleets crewed by such did appear... in late medieval and early modern times. It was the French and the Spanish and the Ottomans who fielded fleets of galleys rowed by slaves. Not the Romans, Greeks and Persians.
I blame Ben Hur for infecting the public consciousness with the "ancient galley slaves" idea.
The Persian fleets in the Persian Wars consisted mostly of Phoenician and Ionian Greek ships, as those regions had strong native seafaring traditions and were subject to the Persians. As such they would have been organised and crewed very similarly to the Greeks. u/DramShopLaw explains here
u/XenophonTheAthenian writes on (the lack of) galley slaves and conditions for rowers on triremes here
u/Iphikrates covers the battles of Artemision and Salamis here