While your eye can't perceive the difference in the actual number of frames, the difference between 24 fps and 48 fps is immense-- and if you have an HD TV, there's an easy way to test it. Find the "motion smoothing" option on your TV, which turns on a system that creates new frames to go between the ones that exist in any normal 24 fps movie you own. Put on the film and watch as it transforms into something surreal and unfamiliar… not bad, necessarily, just totally different. That's the tiny but enormously important difference that frame rate can make.
So how does it work in The Hobbit?
Watching The Hobbit: An Unexpected Journey feels a little like that "motion smoothing" experiment, since it's a movie set in a world we've already seen before in three films. Visiting familiar locations like Bilbo's Hobbit hole, or meeting Elrond again, you're stunned by the difference; in the Lord of the Rings films these people and places felt softly distant, but in The Hobbit they're right up next to you, as visceral as if you'd stepped on to the set. The effect is even more bizarre when looking at full CGI creatures, because it seems impossible that these beasts have wandered into what's feeling like a real place.
Peter Jackson wants to tell us it's a great thing that An Unexpected Journey feels more real, and with good 3D projection and the 48 fps, it's undeniable that you will feel closer to Middle Earth than ever. But there's a huge difference between that and being actually immersed in the movie. I never completely adjusted to 48 fps, to the point that even in the final battle scene, I was distracted by how fluidly Thorin Oakenshield ran into battle. It doesn't help that the technology seems to have a few kinks, and that a lot of fast movement by real and CGI characters alike feels unnatural-- the giant wolves you can glimpse briefly here move as awkwardly as the worst CGI in 48 fps, but look perfectly normal in that 24 fps clip. Dialogue scenes with characters sitting still can almost allow you to settle in, but as soon as Bilbo or the dwarves start running, the 48 fps steals all the attention away again.
By seeing An Unexpected Journey in 48 fps you're essentially allowing yourself to be Peter Jackson's guinea pig, testing the boundaries of an exciting new technology on a movie that might not be best suited for it. I wonder what 48 fps would be like on, say, The Bourne Identity or even Skyfall, movies rooted in the real world that would benefit more from a "you are there" feel. As much as Lord of the Rings fans have treasured their visits to Middle Earth, it's always felt like a far-away place, and it needs to; the 48 fps implicitly tells us that the movie is real, on a soundstage somewhere far away, and that breaks up the fantasy.