2GB is definitely enough for 1080p...
99.9% of the time it is.
However, this guy likes to use the super-high resolution texture packs for skyrim that have almost zero compression.
It just so happens that would be the 0.01% where 2GB of VRAM can be a bottleneck during some scenes.
I tried using the texture pack on my video card, and it eats VRAM for breakfast causing terrible stuttering.
This would be the singular case where 4GB of VRAM would make a significant difference (or even a difference at all for that matter.) over a card with 2GB.