I went from a 6950 to a rx480 recently and I run 1200p. New games like Doom, Civ6, and Xcom2 work great at high settings. You'll probably have to go down to medium settings at 1600p, but it'll still be much better than your 7950.
If you can get the rx470 8gb at $215, go for it. However if you can't, then go for the rx480 for that bit of extra speed that you'll need. This will keep you satisfied for a couple of years then you'll need to upgrade again.