One place where more VRAM helps a lot is when you have an animated/changing environment map layer. When you have little VRAM, there's a lot of time wasted uploading and clearing textures to and from the VRAM; with a lot of VRAM, more can be held on the GPU at once.

 

Also, plug-ins like Element 3D that rely on the GPU perform better (and crash less) with more VRAM.