My phenom is a really old cpu even by 660 ti standards. The fx in question is newer and more powerful. Lots of games do not utilise that much cpu power and if the game is cpu bound, it will be bottlenecked regardless of the gpu so a 1060, if found at $250 will perform better than an rx 480 at the same price. (Just get the 6 gb)
Edit: if your psu is not 80+ rated or is below 400-450 and your total budget is $250, you should totally get an rx 460 + a decent psu. I dont think a 960 is a good idea.