I'd say R9 290X + 390X are 99,9% the same, although Ram clocks are higher (1250 MHz -> 1500 MHz which helps) and GPU clocks a tad as well. Generally R9 390X is 5-10% faster than 290X, but it's essentially the same just with higher clocks.
RX 480 vs. 580 should be the same, just higher clocks - but I doubt they will increase Ram clocks this time, I didn't hear of any GDDR5 spec'ed higher than 2000MHz, though it would certainly help a lot.
Not talking about the cooling here, obviously the R9 390X custom cards are better than most 290X custom cards (I don't care about the AMD ref...).