Protagonist
Character Role Analysis
Odysseus
The book is called the Odyssey, so this isn't exactly a hard choice Homer also makes it explicit that Odysseus is handsome, brave, smart, and an all-around nice guy. Typical classical hero. We also spend the majority of our time following his plotline. We sympathize with him, hate Poseidon for making his life so difficult, and want him to get home already and so he can get rid of all those suitors.
However, Odysseus, like any man (or god, given what we've seen in the Odyssey), has flaws—one in particular: hubris, or excessive pride. This that gets Odysseus into trouble several times with both mortals and immortals, imperils his journey, and complicates his difficulties—but it also makes an ideal protagonist: one with something to learn. (We hope.)
Telemachos
Telemachos may not get as much screen time as Odysseus, but in some ways he's a more interesting character. (See his "Character Analysis" if you want us to convince you of that.) Odysseus may be a typical Greek hero with his excessive pride, but Telemachos just might be a much more modern hero: whiny, ineffectual, and with major daddy-issues, he has to go on a vision quest to find his father before shaping up into a leader—just like Luke Skywalker. (Which makes Athene Yoda.)