I don't know very much about Persian inscriptions (although the only inscription of Xerxes to my knowledge that mentions the Greeks at all is the Daiva inscription, which simply lists the Yauna on both sides of the sea among the people that Xerxes rules) but Athens was certainly destroyed. There's a layer of debris at Athens called the Perserschutt (lit. "Persian rubble"). If you've ever been to a museum with classical sculpture you've almost certainly seen items from the Perserschutt--most of our Archaic Period statues survive because of it, and pretty much all of our early Classical vases. The stone rubble was incorporated into larger buildings (or sometimes buried), especially the new Themistoclean Wall, and the smaller rubble (particularly smashed ceramic items, which would not have been destroyed by fire) was mostly buried or dumped into wells. Most other objects would not have survived the destruction of the city. I'd be interested to know where this account of the capture of Athens is. To my knowledge no Persian inscription mentions Athens by name. The concept of "liberating" a city is generally considered to be a 20th century one, and the claim that Xerxes allowed the Athenians to retain their religion is an...interesting one. The Daiva inscription explicitly mentions him destroying the temples of demon-worshipers, which indicates no qualms about destroying temples, and the fact that a high proportion of the objects in the Perserschutt comes from temples on the Acropolis that were demolished has long been taken as an indication that the Acropolis was cleared by the Persians (which appears archaeologically backed up by the foundations there, though archaeology of the Acropolis is made difficult by the presence of the Parthenon)