The 960 is much more powerful. If you want the best price/performance, the R9 380 is faster than the 960 and usually the same price or less. However, I suggest waiting until June 28th. AMD will be releasing the Rx 480, 470 and 460. The 480 is rumored to be between a 970 and 980 in performance. The 470 should be around your price range and it believed to have between 960 and 970 performance. But we wont know for sure until the 28th.
If you prefer nVidia, at the very least the AMD cards should reduce prices.