More memory will not help out for the jagged shadows. Shadows are not textures stored in memory, they are calculated in real-time. So you'd rather need more cpu/gpu cycles than memory.
I'll try to stop the smart-ass-ness now
That's correct, but remember what the shadows are projected as, and what they're projected from.
Also consider the possibility of some re-allocation; what may previously have had to be generated, could now be pre-made and stored.
Wrong, and Wrong. I'll make this simple for the people trying to out-smartass the guy who was right in the first place.
Everything rendered on your screen is stored in memory.
The shadows used in GT5's cockpit view are clearly shadow maps because they are low-quality and have no anti-aliasing.
Ray-traced shadows would take too much processing power and memory to achieve in a game engine.
Shadow maps are usually the low quality option in 3D content creation but for games they are what is most commonly used.
Shadow maps ARE textures.
The way shadow maps are calculated is complicated but let me break it down for you:
A shadow map is created by rendering the scene from the view of the light source and checking whether a pixel is visible from this view by comparing it to a z-buffer (which is stored as a texture).
An important part of the quality of the shadow map is the quality at which the picture is rendered from the lights point of view. Since this AND the depth map both need to be stored in memory, they are directly affected by how much is available. The more memory, the high quality the shadow map can be rendered at, because the depth maps can be rendered and stored at higher resolutions.
A shadow map is calculated for every frame of the render.
In a game this means that the shadow map must be recalculated for every frame. In most games this is 30Hz or 60Hz.
Since the shadow map is rendered outside of the actual rendering you have a game that runs at 60fps but shadow maps that update 30 times a second, at which point you will have a more jittery shadow map in comparison to the rest of the game.
I've seen this happen many times in many games.
Anti-aliasing shadows again means more memory, since a much higher resolution render of the shadow map needs to be done in order to sample the images.
I hope this was enough smart-ass-ness for you.