Uhh, I believe it actually mostly relies on the RAM. But I don't know for sure, the more RAM you have, the faster the Renders.

i thought it depended on cpu, ram, and gpu. also CUDA benefits a lot in adobe products. i currently have a gtx 460 which doesn't have much cuda cores paired with an i3 processor and my render speeds are still quite fast.

if you have a nvidia graphics card i am sure cinema 4d benefits from it but not Photoshop. and yes you would see a render speed difference as a gpu can do more calculation per second

C4D render speed is almost completely dependent on the CPU. The GPU is completely unused. Having more memory will not necessarily improve performance and if the program isn't using all RAM available to it, more would not affect performance at all. If all the memory is used and more is needed, the program will use a drive instead, decreasing performance. RAM usage depends on the task.

For Cinema 4D it's definitely CPU-based rendering, A graphics card would probably help in the non-rendered aspect, While modeling and setting up the scene.
After effect or sony-vegas rendering, Is mostly RAM and GPU, GPU to actually render the frames and RAM to cache them for faster more streamlined playback while editing, As for rendering/encoding, probably the same.(GPU+RAM)