Do you prefer Homer and his two epics — The Iliad and The Odyssey — or Shakespeare?
For me, Shakespeare is the greater and broader writer - more depth to his characters, a kind of invention of the "human" as we know it (though this is prefigured, IMO, by the Hebrew Bible's depiction of personalities like Jacob and David), poetic language that contains metaphor and simile, and a comprehensiveness of vision that accepts comic, romantic, and tragic all at once. Hamlet, King Lear, Macbeth, Cleopatra, Prospero, Shylock, Portia, Viola, Malvolio, Brutus, Iago, Edmund, Edgar, Cordelia, Richard II, Falstaff, Hal, Antony, Othello, Lady Macbeth, and more - all these rich personalities that Shakespeare creates with a richness that is challenged only by the Bible IMO.
As for Homer, however, he deserves his place as the king of poets besides Shakespeare. I find The Iliad to be as refreshingly bold, violent, brash, big, and beautiful as it was when it was first read and loved by ancient audiences. I love the fierce pathos and charisma of Achilles, the wily genius of Odysseus, the defender-of-homeland love of Hector, the pity of Priam, and more. Characterization is more lucid, less "complex" in the way that the Bible and Shakespeare are, more transparent. The divine and human interplay makes the work so fascinating, as do the questions of heroism. To be honest, I consider Achilles my favorite hero of the Homeric universe, next to Odysseus and Diomedes, with Hector being admittedly before both wily heroes.
Yet I find Homer's narrative work so eloquently dramatic - sixty percent of The Iliad is dramatic dialogue - and powerful in the epic similes and violence that it remains in my memory as a thing of beauty, a joy forever.
Of course, The Odyssey, with its protean Athena slipping and changing into various human forms, its wily and Jacob-like Odysseus (Jacob is the great "survivor" of the Bible, and Odysseus might be a kind of Hellenic Jacob due to the endurance he shows), its narrative-within-narrative experiments, its treatment of stories, its Orestes-motif with Telemachus journeying away on a coming-of-age adventure before returning to slaughter the evildoing suitors, the near-Asiatic emphasis on a god's personal relation with a human (reminds me of Gilgamesh), its fairy-tale riches-to-rags-to-riches again, and more.
So I give the preference to Shakespeare, but a very very close second to Homer.