I watched LotR last night and the same question sort of popped in my head. I recall in "The Hobbit" there was some mention that the world looked blurry or washed out, or something, when Bilbo wore the ring.
When he first puts on the ring in Gollum's passage, he doesn't notice anything at all. He's suprised when Gollum runs past. He also wears it for a long time without problem or comment in (for example) the Elf Kings fortress.
I would say that Jackson perhaps overstated the effect on the mundane world, probibly in order to give a visual way for us to understand a feeling described in LotR.
As to the reason that the feelings and impressions of the ring bearer are different from the Hobbit to LotR? Because the worl is different. In Hobbit, Sauron is arely capable of manifesting (is, in fact, in hiding as "the Necromancer" and is defeated by the wizards during the course of "the Hobbit"). So Bilbo does not feel the pull, because Sauron (of whom the ring is part) is not powerful.
Similaraly, the power of the Nasgul is directly related to Sauron's growing power.
This also explains how Bilbo went so very long with the ring with very little ill effect. (Gollum was just an obsessive kind of guy, most of his obsession was not the actual control of the ring, which Sauron comments had suprisingly little control of Gollum)