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No, there's a very big gap between the 960 and 970. No need to use "common sense" when you can use facts and benchmarks! ;) The 970 is over 30% faster than the 380X at 1080P and 1440P, which is about the difference between 40-45FPS and 60FPS.
Using common sense, if the 380 is about 5-10% faster than 960, then this 380x can't be too far off a 970? oO Seems a great deal, this is much better than the lowly 460, but would recommend getting a 470 is you can spend a few bucks more.
It's a good price, if you can't fork out for the basic RX 470 @ £165. Though I would advise to go for the better RX470/480 or GTX1060, for the extra £30-£60
You're right, there's generally a big gap between them with the 970 way out in front. The OP's also right, there are a couple of scenarios where the 380X does catch up to the 970. Hitman in DX12, for example, the 970 just barely noses ahead at 1080P, and then the 380X just about beats it at 1440P! Extremely rare scenarios, but they do exist. So everybody's right! Hooray! We can all be friends! :)