Gloss - The X360 version sports a few graphical enhancements, among which is the inclusion of a superfluous gloss effect for the characters.
Achievement System - There is an Achievement list for the X360 version, a common thing for games of this console. By completing certain tasks, the player is awarded with Achievement Points. That list can be viewed here.
Multiplayer Battles - The PSP version has exclusive multiplayer battle arenas, where up to 4 players can fight each others. The arenas are Jungle, Factory, Ice, Desert and Cave.
Graphical Limitations - The PSP version lacks a lot of the graphical details from the other versions. Notably, Crash lacks a shadow, which makes it harder to jump between platforms.
Tiny's Model - Tiny has a different model on the PSP. It is much less detailed and its eyes are just red dots with no sclera.
The Disappearing Mask - If you Jack a Titan in the PSP version, pause the game and then unpause it. Aku Aku will disappear from the Titan's face.
Loading - The Xbox 360 version has the word "LOADING" along with the footprints.
Tutorial Drawings - The Wii version has drawings of Crash and the Titans in each tutorial page.
Missing Sound Effects (by Concept Window) - The PSP version is missing some sound effects, such as those for attacking and spinning.