The differences between the two “worlds” are easier to list than the similarities: different genres, different centuries, different religions, different governmental systems, different state/country make-ups, etc. But the two worlds are alike in that they come down to us as literary constructions, with details chosen by authors, not just by historical facts. The Greek/Trojan story is known to us by historians of the period, and Homer embellished and selected those details that suited his purpose. Shakespeare, in using Froissart’s Chronicles as a source of Hamlet, as well as other histories of Denmark and the Scandinavian territory, also chose those details that served his dramatic purpose. Also, both pieces have become staples of western culture, drawn upon by subsequent generations; Shakespeare himself drew from the Iliad to write Troilus and Cressida, and, of course, Hamlet has fed many pieces of writing -- Stoppard's Rosenkrantz and Guildenstern are Dead, for example. Particularly important are the details of ruling: kingships vs. war leaders, etc.