A disclaimer here: while I have been known to read and enjoy poetry, I claim no particular discernment. I just know what I like, and generally why. But I can't tell a villanelle from a viola without a dictionary.
What is interesting to me is how related skills can come together in different ways for prose versus poetry. Both require a sense of language, meaning, a good vocabulary used thoughtfully, etc. But the whole is definitely greater than the sum of the parts. I think the awareness of turns of phrase which is useful in, say, a work of fiction becomes of paramount importance in a poem.
I once interviewed a brilliant guy, a VP of Sales, and as I usually do, I asked him for specific events in the recent past to get an idea of what he did, and probed unmercifully to find out details. (It's called a behavioral interview, and it's actually nicer than it sounds.) Only when reading the transcript of this nearly three-hour interview did I realize that he had carefully structured the whole interview as we did it -- there was an organizational principle that governed all the stories he had given me, a framework that he had evidently used to pick out which stories to tell, to illustrate a larger point he wanted to make about his job. It's hard to do that on the fly -- and even harder to see it when you are working at interviewing, I might add. I think poetry might be like that -- at its most extreme, with every word is potentially organized against every other. In prose, you follow a thread, and the overall style and flow must be compatible, but for most writers I don't think every word counts in precisely that way. In fact, some authors like novels exactly because they are looser, whereas a short story requires discipline, and a short-short requires fantastic organization and discipline to pull off.
This may explain why most poems are considerably shorter than a lot of prose works! Unless you are willing to work seventeen years on a work as James Joyce did on Finnegan's Wake, you are unlikely to craft every livin' word of a novel!
But I also suspect that there is a limit to how much your brain can hold. Or at least mine. My mystery writer wife Toni can hold multiple plotlines in her head and tinker with them -- a very useful skill for a mystery writer. I am far more linear, which lends itself to explanatory prose or to telling parables, but not so much to deceiving the reader. Some poetic structures require you to look at rhythm, alliteration, scansion, words and definitions, puns, and rhyme. Yow! Try doing all that at once.
In the same way that mysteries often emphasize plotting, romances character, and science fiction setting (yes, I know I am grossly oversimplifying), I suspect poetry emphasizes the language itself. Which means, from my motivational point of view, that it may be necessary to get a lot of motivation to propel a relatively small quantity of words.
Any thoughts on this are welcome!