Look, I just bought a 4GB GTX 960, and I did my research before buying.
R9 380 vs GTX 960 (assuming both 2GB models):
- Cons for R9 380: It runs hotter, it produces more heat, and it requires substantially more power to run. If these are not a factor for you, then disregard this con.
- Pros for the R9 380: It has got on the whole better performance compared to the GTX 960. In DX12 games especially, it can be up to 20% faster. With DX12 looking like the future, the R9 380 would in this regards be the better purchase.
2GB vs 4GB:
- For those who say 2GB is enough for 1080p gaming, nonsense. We already have games hitting 4GB at 1080p. The MAJOR benefit of a 4GB VRAM card is that it should allow you to play at ULTRA texture settings in the short term, and at high texture settings in the medium to long term. Textures can make a game look good or ugly. I play TW3 at medium preset + ultra textures, and it uses 2400MB of VRAM. I also play Everybody's Gone to the Rapture at Medium + Ultra textures, it uses 2800MB of VRAM. I play Hitman at Medium + Ultra textures, it uses 2700MB of VRAM.
4GB VRAM also gives about a 5-10% performance boost (depending on game) and it will be almost impossible for you to stutter in games due to the VRAM buffer maxing out.
4GB VRAM will of course future proof you, 2GB will be dead within the next year or so for AAA 1080p gaming.
OP, get which is cheaper and see which fits your use case scenario better.
EDIT: OP, you should STOP looking at those useless 2GB vs 4GB benchmarks. Most of the games being tested are pre-2015 linear games in there. The future is open world, no more linear. And in open world games, 4GB WILL make a difference. Trust me on this. Lack of stutter plus slightly higher regular framerate. I can confirm this from my own experience.
See this 2GB vs 4GB Rise of the Tomb Raider comparison:
https://www.youtube.com/watch?v=iA-vOSAsOhs