Depends on the games you are playing, and if you care about power consumption/ heat.
The 960 and 380 in terms of raw performance will trade blows with each other depending on the game and situation.
The 2gb of vram could be a problem depending on the games you are playing, as games like gta 5 will use much more than that, however there is a 4gb 960 that you could possibly pick up for a similar price.
The 380 will consume more power, costing more, and therefore put off more watts of heat.
I would say go for a 4gb 960, or the 380. If you can get a 960 that is within $20-30 of the price of the 380, i would go for it, for reasons of power consumption and today Nvidia has a handle on most of the games, making their cards work better than AMD's. Otherwise, go for a 380.