Interesting question - not sure if perhaps it hasn't been addressed in Tolkien's letters (anyone knows?) or something, but I would say that it has to do with the "degree of corruptedness" of the person, first; second, maybe also the rising power of Sauron caused the Ring to have "stronger influence". Also, Frodo started seeing the stuff mostly after he had gone through the experience of being almost stabbed to death by a Morgul-blade, and Sam saw that only in Mordor, where the power of the Ring was certainly altered considerably...
But that is just my own guess.
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"Should the story say 'he ate bread,' the dramatic producer can only show 'a piece of bread' according to his taste or fancy, but the hearer of the story will think of bread in general and picture it in some form of his own." -On Fairy-Stories
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