2GB of VRAM is generally sufficient for 1080P, only skyrim with a bunch of mods will need more than that. The 4GB versions are meant for people who want SLI or CF since it only behaves as though it has as much memory as the smallest card, but for a single card setup you simply don't have the power to run a high enough resolution with AA to need more than about 2GB of memory.
The statement about BF4 being fine and watch dogs being choppy is poorly researched, Watch Dogs is significantly CPU limited, it doesn't require a GPU with a lot of VRAM
http://www.tomshardware.com/reviews/watch-dogs-pc-performance,3833-8.html