its not about not working, and it is a technicality, you need to understand texture memory.
Artwork has to be loaded into the video ram to be drawn to the screen, artwork like the paint on the sides of models or the texture drawn on the surface of walls or water. These are loaded when the game starts because you cant see anything without it. Not all of them fit, because modern games have gigabytes of art files, but you only need to have as much as you can see at one time and the game will intelligently swap out and back when things will not be used. (the badguys from level 5 dont have to be rendered during level 3). Having more vRam will give you a smoother experience. A good example is Oblivion where indoors and outdoors have different art files, so having the 256 will make transitions smoother.
Also, a big impact is the fancy graphical settings of Antialiasing and anisotropic filtering. These expand textures to look nicer and smoother, not framerate wise but in a single screenshot. They also then require 2x or 4x more texture memory, and you hear about big videocards being able to play whatever game on 'max settings' because it can handle that.
the 128 and the 256 have the same gpu so they draw the same speed, but the 256 can do it with more antialiasing and smoother between 'rooms'.
For professional work, like some kind of 3d AutoCAD, that 256 videoram will allow you to have twice the complexity on one project with no slowdown. The software called Motion does this as well.
so 256 isnt actually faster, but it is still better
Edit: I almost forgot to get to the point; There are no games that will run on 256 but will not run on 128, theyll just be capable of being prettier under 256.