We often hear or read a poem and invent a story about it, too. These writing genres don't exist in a vacuum--there are "narrative" aspects to poetry and poetic aspects to narrative.
I think the question is better framed in a different literary split: epic versus lyrical. Epic poems, novels, etc. all have a grand sweep to them -- you can't understand one part without the rest, and the full weight of the artistic message is only realized by experiencing the whole work.
Lyric poems, on the other hand, are small personal snippets. They are often more subjective, more personal, and while these poems are usually collected in volumes, each poem is a complete work unto itself. True, you can compare and contrast different poems to come up with larger meanings, themes, etc. but the basic purpose of the lyric poem is to be an independant artistic work.
Now, think about photographs. You can see one Ansel Adams print and understand the print completely -- viewing other Adams prints is nice, but not really necessary to understand the one you are viewing. Each photograph is a separate act; even in a series, photographs receive their power from the essence of the lone still picture. The rhythms and contrasts within the photograph itself are part of the message, just like the cadence and rhyme within a poem are part of its art.
Film, as in cinema, on the other hand, is definitely a more epic medium -- we anticipate from one moment to the next how all the moving images in front of us relate to the larger picture.
So, if I have to use what I believe are oversimplified terms -- poetry or narrative -- I would say that still photography is definitely more poetic.
