Situation-independently, which of these items are better suited for Nature's Prophet, and why?
I'm going to disagree with both of your potential answers and instead suggest Medallion of Courage. While it doesn't increase your attack speed or damage, it does serve the same purpose of allowing you to gank by lowering armor. Nature's Prophet (when played properly) is an extremely strong ganker as he can be anywhere on the map at once. His pushing will obviously be weaker as this doesn't affect buildings, but you can easily pick up one of the other two items later.
Medallion gives him the single target focus that helps him gank and also allows him to more easily kill Roshan in the early game. The only time I would consider it a bad pickup would be against many heroes with high base armor or many agility heroes, as their armor rises much faster in the early game as they gain levels.
My choice would be desolator it is cheaper and easier to make and when it is done the damage boost will make ganking,farming and last hitting much easier.
Cuirass is a good pushing item it makes "creep combat" faster,attack speed and -armor stacks nicely to desolator,but buying it before desolator or completely without it wouldn't be the best choice for furion.Also since it is combat aura for maximum effect it would be more suitable for high HP heroes that can stay longer in middle of fight.
But given enough time you will most likely end up with both items since they make good combo on Furion.