I've been reading several Near Eastern general history books and they all end around 500 BC. My understanding is that the Hellenistic states weren't all that different from earlier Iron Age empires. Was there really a substantial difference that warrants such a sharp delineation between the ancient period and the 'classical' period in Near Eastern history?
I'm not sure I understand your question. The Hellenistic period begins in 323 BCE (not 500), upon the death of Alexander and the fracturing of his brief empire into dynastic kingdoms ruled by his successors (the diadochoi), e.g. Ptolemy in Egypt. For the Near East, the majority of the territory would eventually fall under the dynasty of the Macedonian Seleucus, marking a paradigm shift and a convenient horizon of periodization when writing history textbooks.