Some levels from Story Mode were taken out of the American version, and a few were given different winning objectives. Some cutscenes in the GC version play no music at all, while (almost) all cutscenes play music in the PS2 version.
There are a few cosmetic changes to the HUD as well. The icons of the mamodo in the Japanese version are removed, the indicators merely showing the character names instead. Also, in the Japanese version in Story Mode, character reactions are visible in both up-right and down-left screens. However in the U.S. version they don't appear, although some of the dialogue remains.
Since both the PlayStation 2 & GameCube have different graphic rendering, there are many differences between the lighting, rendering and textures on both versions.
Source: Wikipedia, "Zatch Bell! Mamodo Fury", available under the CC-BY-SA License.