The RX 580 will do ~315 H/s on ZEC. The Claymore epoch benchmark figures are just an estimate and largley overstated. In my own test with a five card RX 480/580 8GB and 570 4GB rig. The benchmark at epoch 129 for the five cards was ~143.3 MH/s, at epoch 130 the benchmark was ~142.5 MH/s. The actual current dual mining hash is ~144.1 MH/s dual mining with DCR. Even a 10% drop in the RX cards ETH hash in 6 months can be offset by addding a single $200 RX 570 4 GB card.
Where does the huge difference on ZEC mining coming from between 1070 and rx580?
At ETH a GTX 1070 has similar MH/s than the RX580 but at ZEC it has 50% more (~ 480 Sol/s). From gaming perspective they are also very similar from performance.
And yes, this is a serious question as i'm interested in technical details due to my work in IT business

ETH and derivatives are very "memory hard" due to the algo used - and as AMD 8GB RX-series cards have the SAME memory clocks and bandwidth as GTX 1070 cards, they end up being similar in hashrate when the memory access is optimised (the NVidia cards seem to use higher-performance memory settings by default in their BIOS than AMD uses).
Other coins mostly use algos that are more core-limited, so the higher clocks on the GTX 1070 and similar number of cores vs the RX 470/570 make the 1070 quite a bit faster (the 480/580 have higher core count but clock a LOT lower, so the 1070 still wins there).
What about 1080? Ofc electricity is an issue, but anyway. U can buy it for cheap in Europe