In terms of raw power R9 380 is a bit better than GTX 960. But GTX 960 uses a lot less power, runs cooler etc. And by buying an AMD card you will be missing out on certain Nvidia exclusive features like Gameworks, Hairworks, weapon debris effect (fallout 4) etc.
Also Nvidia has much better drivers than AMD, with upcoming drivers you might expect GTX 960 to become better and better.
Furthermore, GTX 960 can be used for other tasks as well like video editing, rendering on which AMD isn't that great.
Some 1 day ago, I was also thinking to sell my GTX 960 for R9 380 but after some research changed my mind. Rest be assured, Nvidia will never let you down, they have a very good rapport with many AAA game developers on which Nvidia cards...