I agree that many free verse poems are more prose than poem.
Entirely in my own conceptualization of what poetry is:
Line: I believe the line is important, whether it has rhythm or rhyme is only a factor. The line should contain a thought, not just part of a run on sentence, but a whole thought in itself. Moreover, each line should lead to the next line as thoughts in a rumination, a baring of the soul or even a day dream.
Stanza: The stanza is one whole part of a monologue or dialogue. It has a beginning, development and an end, like a paragraph. Unlike a paragraph each line should make you understand a single concept. Taken as a whole, the stanza suggests something more: perhaps it is a paradigm, perhaps nothing more than an opinion, but is a separate chapter of the work.
Poem: The whole poem to me a a dialectic. It subtly or obviously presents an issue, be it some concern about a relationship, a choice that must be made, reminiscing about an event, or the quiet observation of a scene, or anything else. There is an answer to the issue, either by developing it, countering it, setting up a tangential movement or such. Finally, there is a resolution, a synthesis or conclusion. The issue is now fully presented in a manner that takes the reader on a journey - emotional, intellectual or intuitive.
What makes it different from prose, in my world, is that you could not possibly speak this poem in normal conversation. It requires attention to each line, to each stanza. It demands recognition that the concept is broken down into parts which must play against each other. The use of rhyme and rhythm is an aid to this purposeful deconstruction of communication, but neither is a requirement in itself.
All of these thoughts are wholly my own and I do not in the least claim to be an expert.
Moreover, the exceptions to this process are quite often more poetic than the slavish adherence to it.