Desires address a single goal or object, and grant it an absolute weight on the scale of utility: "X is worth 5 utils to me." (We may write "|X| = 5" for short.) Preferences, in contrast, are purely comparative: "I prefer X to Y." These two types of states are presumably interdependent: in particular, I should prefer X to Y iff |X| > |Y|. But which is more fundamental?
Desires seem more basic, being monadic (taking just one object) and scalar. So I'm inclined to see comparative preferences as merely a fancy way to report relative desire weightings. But that would render intransitive preferences not just irrational, but strictly impossible. To prefer X to Y, Y to Z, and Z to X, is not possible for any combination of desire weights |X|, |Y|, and |Z|, for the 'greater than' relation is transitive. But isn't it possible that someone really might be disposed to pick X when offered X or Y, pick Y when offered Y or Z, and to pick Z when offered Z or X? Our motivational systems are messy and context-dependent in all sorts of ways that the simple desire model fails to capture.
Might we instead define or construct desires out of preferences? This would be a lot messier. We've already seen that in case of intransitive preferences there would be no coherent way to assign absolute weights to each individual desire. But so long as the preferences satisfy the standard formal requirements (transitivity, asymmetry, etc.) it might work out better. Though it's not too clear how to assign scalar values to a mere ordering of more and less preferred outcomes, one might suggest that the scale of "utils" never had any clear meaning in the first place.
Most likely neither option is wholly adequate, as it seems unlikely that either desires or preferences have exact neural correlates. They are what Dennett calls "real patterns": useful abstractions (like centers of gravity). It's unsurprising, then, that such models break down when we push them too far. I expect that desire talk will usually be more useful than preference talk, at least. Are there any other competitors for modelling human motivation?