I play Crysis 3 at 1440p and high settings on a GTX 770 4GB, and it runs just fine. Crysis 3 isn't a VRAM-intensive game.
http://www.digitalstorm.com/unlocked/video-memory-usage-at-4k-uhd-resolutions-idnum146/
VRAM usage is entirely dependent on the individual game. Typically, open world games such as Far Cry 4 and GTA 5 are VRAM-intensive as the entire world has to be rendered with no loading screens. A game like Metro 2033: Redux, which is considered a graphical powerhouse, uses very little VRAM as only small sections of the game are rendered at a time.
We don't know that the OP is considering the GTX 970 and R9 390, but there's a good chance they are. Performance between the two is very similar at 1080p and 1440p and the advantage comes down to the individual game.