The vast majority of VRAM is used to hold textures. For 1080p gaming, there's not much need for higher resolution textures than high (1024x1024). 2GB is enough for the vast majority of games using high textures. Higher amounts of VRAM are mostly needed only if you go up to ultra textures (2048x2048), and you'll only be able to see the difference at 4k or if you take the time to look really closely at a texture (e.g. move real close to a tree or wall) at 1080p.
That said, some of the newer games are really pushing technology with tons of textures. Even with high textures, they can exceed 2GB. So there is some argument for getting 4GB of VRAM even at 1080p. I'm not sure it's worth $30 extra. I think I'd rather pocket the money so I could use it on a new GPU in 2-3 years. But if you're planning to use this GPU for the next 4+ years, then the extra $30 is probably worth it.