On GPU front until you are getting the gtx960 4gb for about the same then it doesn't matter. But, if the difference is more than there is no benefit with 4GB on gtx960 as the GPU is quite weak to make use of more than 2GB RAM.
Also, the above benchmarks that you have pointed to shows that only at 1080p resolution there is sight bump in fps from 2gb to 4gb and that too in a single assassin creed game. Other benchmarks clearly shows that 2GB is slightly faster than 4GB version which again is irrelevant.
Looking at the fps data for other games in the comparison. I would put the assassin creed data under suspicion whether that slight lower fps on 2gb version was really due to the RAM. Also again at 1440p we see the same result that there was no difference between 2gb and 4gb version in assassin creed.
Anyhow, gtx960 2gb and 4gb makes absolutely no difference as the gpu is not powerful enough to handle more. So, I would recommend that if you get the 4gb for similar price only then consider it otherwise you can also look at 380 for better performance.
I wouldn't call the jump from 26fps to above 34fps 'a slight bump' . It may look like just 8fps but to the eyes its the difference between smooth gameplay and stutter. You can test it with any game on even older hardware.
If you look at the latest batman game, it is also affected by whether you have 2 or 4gb of vram. Moreover, it actually performs better on Nvidia hardware than AMD because of increased CPU overhead of AMD cards which is commonly occuring issue with DX11 games.(Performance Analysis: Batman on PC is still a disappointment • Eurogamer.net)
Shadow of Mordor is another one which is affected the amount of vram, although because AMD was involved with its development, it performs better on AMD hardware.
Furthermore, RPG games,which the OP wants to play, as they get older tend to get more mods which include graphical updates that require more vram. Skyrim is a good example of this even though its dx9.
As for the AMD 380 vs Nvidia 960, I would go for Nvidia,even though its a slightly less powerful card. That's because Nvidia's drivers are much better quality. Therefore, even with a weaker card, Nvidia's perform as good and more consistently than AMD's. For example, frame pacing is often an issue with AMD cards unless they are combined with a powerful CPU.
Another point, which I am not completely sure about, is that the AMD 380 requires 2 power connectors for which you either would need to get a convertor or a different power supply. You can search for a single connection AMD 380 but that's just another hassle to be honest considering how very small the performance difference is between the 4gb 960 and 380.
OP, if you are willing to, I would strongly suggest you look up the price of a Nvidia GTX 970 and see whether you can and would like to save up the money to buy that. THAT card will give you a great experience now and in the next 3 years or so.
