The Odyssey is the archetype for an entire genre of "road trip" stories throughout history. It's also, more broadly, a key point of influence for many aspects of the Campbellian hero's journey. The Iliad simply hasn't exerted the same level of influence on storytelling.
The roadtrip part is smaller part of the Oddysey (maybe 30% definitely less then half), most of that is politics at home and getting control of the house. It is much different then other example of the narrative structure listed as examples of hero's journey.
That’s probably true, The Odyssey is a coherent story with a single protagonist and works better as a whole narrative. The Iliad is really a collection of stories, but taken together it’s a treasure trove of characters, events and ideas.
The Golden Apple, the beauty contest of the goddesses, Helen’s elopement with Paris, the Greeks burning their boats, the story of Achilles and his famous vulnerable spot and death, the wooden horse, the destruction of Troy.
Its a huge fund of anecdotes, sayings and archetypes that infuse western society.
Most of the stories you mention in relation to the Iliad don't actually appear in the Iliad, you know.
Also, if anything can be described as "a collection of stories", it strikes me that Books 9-12 of the Odyssey (Odysseus' stories about the Cyclops, the Laestrygonians, the Lotus-Eaters, Scylla and Charybdis, the Cattle of the Sun, etc.) fit the bill much better than anything in the Iliad.
"The Iliad simply hasn't exerted the same level of influence on storytelling."
This is highly subjective. The influence of the Iliad on European literature, art, and culture has been absolutely colossal.
Indeed, given that the Odyssey was itself influenced by the Iliad, you might say that anything the Odyssey influences should ultimately be credited back to the Iliad.
