The R9 380 is usually a bit cheaper and bit faster than Nvidia's 960. There isn't much in it though, so I would suggest buying depending on what bargains you can find on the day as either card should do you well. In both cases, try and get a 4GB card as offers can make them down under the £150 mark that not-on-offer 2GB cards usually live at.
If you are considering a new monitor in the lifetime of the card, the R9 380 can do FreeeSync which is worth having. Nvidia Gsync adds £100 to the monitor price and the choice is rather more limited. I don't think that should be a deal breaker, but might be a nice bonus in favour of the 380.