Phoronix published interesting benchmark results for OpenGL vs Vulkan on Linux, across a wide spread of thirteen NVIDIA GPUs. Before we begin, the CPU they chose was an 80W Intel Xeon E3-1280 v5, which fits somewhere between the Skylake-based Core i7-6700k and Core i7-6700 (no suffix). You may think that Xeon v5 would be based on Broadwell, but, for some reason, Intel chose the E3-1200 series to be based on Skylake. Regardless, the choice of CPU will come in to play.
They will apparently follow up this article with AMD results.
A trend arose throughout the whole article. At 1080p, everything, from the GTX 760 to the GTX 1080, was rendering at ~101 FPS on OpenGL and ~115 FPS on Vulkan. The obvious explanation is that the game is 100% CPU-bound on both APIs, but Vulkan is able to relax the main CPU thread enough to squeeze out about 14% more frames.
The thing is, the Xeon E3-1280 v5 is about as high-end of a mainstream CPU as you can get. It runs the most modern architecture and it can achieve clocks up to 4 GHz on all cores. DOTA 2 can get harsh on the CPU when a lot of units are on screen, but this is a little surprisingly low. Then again, I don't have any experience running DOTA 2 benchmarks, so maybe it's a known thing, or maybe even a Linux-version thing?
Moving on, running the game at 4K, the results get more interesting. In GPU-bound scenarios, NVIDIA's driver shows a fairly high performance gain on OpenGL. Basically all GPUs up to the GTX 1060 run at a higher frame rate in OpenGL, only switching to Vulkan with the GTX 1070 and GTX 1080, where OpenGL hits that 101 FPS ceiling and Vulkan goes a little above.
Again, it will be interesting to see how AMD fairs against this line of products, both in Vulkan and OpenGL. Those will apparently come “soon”.