Sapphire is one of the best of the AMD cards. But if she games at 1080p and likes to use higher gfx settings in-game, go with the 470. The RX-560 is basically a re-branded RX-460 with a few minor tweaks.
Still... if cost is the deciding factor, the 560 is
able to keep most games above 30 fps at 1080p if that is satisfactory. You probably have already done the comparison research, but here's an example (not necessarly the games she plays): https://www.youtube.com/watch?v=tiBqHiA0AZA