First and most obviously, the Wii version's graphics won't be as pretty. Aside from that, though, some of the environments had to be changed, and according to Klepek, some new levels were constructed for Alone in the Dark Wii. (We assume that means there are new levels remodeled on the old levels, not that there are new levels.) For example, Central Park is a large, open world on the HD systems, whereas it's not on the Wii. With changes in the environments also came slight changes in the story, but we're not sure how significant these alterations are.
You can also expect some gameplay elements to disappear, like dynamic fire. Things can still light on fire, but not, uh, dynamically.
Losing the open world scenarios is what hurts the most, but the other changes don't seem too bad. Are these cuts enough to scare you away from the Wii version, or is it all just sausage to you?