The Tomb Raider Linux port is at least one of the games where RadeonSI has been well optimized for it and here the Radeon RX 580 comes out ahead of the GTX 1070 but not too much better than the RX 480.
With the open-source Xonotic first person shooter game, the Radeon RX 580 pulls ahead of the GTX 1060 and just over the GTX 980. Xonotic is one of the better cases for showing the RX 580 over RX 480 where it had a 20% advantage.
With Unigine Superposition, the RX 580 was just frames faster than the RX 480.
Unigine Superposition hasn't received much testing/optimization work yet by RadeonSI Gallium3D drivers.