The DS version is the first version of The Simpsons Game I played, and there are distinct differences between it and the console version. The game itself is a 2D platformer, and the cutscenes are rendered in 3D. But the 3D is not done particularly well and the emotions of the characters in the moment are hard to discern.
While the story is the same, the level structures are different and some just are not present at all. For example, in the Game Engine or whatever it was that followed the Will Wright bit in the console version you have four levels: NeverQuest, Medal of Homer, Grand Theft Scratchy, and the JRPG one I forgot the name of. Medal of Homer and Grand Theft Scratchy are not on the DS version. One could make the argument that it is 'cos there are JRPGs and Zelda games on DS and there weren't any FPS games like Call of Duty on it or GTA games, but NeverQuest is not exclusively Zelda related as there are references to other fantasy-style games, including a direct reference to and parody of Gauntlet and GTA Chinatown Wars exists, though it came out in 2009 while The Simpsons Game came out in 2007, granted. Also the three-part alien invasion thing that references old Treehouse of Horror segments are one level in the DS version and not 3 separate levels like the console version. The final boss fight is different as well as far as gameplay goes. When I finally got around to seeing the console version, I noticed its superiority immediately. The game is fine, but you'll have a better experience with the console version.