We haven't yet benchmarked DOOM on Vulkan Update (immediately after posting): Ryan has just informed me that, apparently, we did benchmark Vulkan on our YouTube page (embed below). I knew we were working on it, I just didn't realize we published content yet. Original post continues below.
As far as I know, we're trying to get our testing software for frame time analysis running on the new API, but other sites have posted framerate-based results. The results show that AMD's cards benefit greatly from the new, Mantle-derived interface (versus the OpenGL one). On the other hand, while NVIDIA never really sees a decrease, more than 1% at least, it doesn't really get much of a boost, either.
Image Credit: ComputerBase.de
I tweeted out to ID's lead renderer programmer, Tiago Sousa, to ask whether they take advantage of NVIDIA-specific extensions on the OpenGL path (like command submission queues). I haven't got a response yet, so it's difficult to tell whether this speaks more toward NVIDIA's OpenGL performance, or AMD's Vulkan performance. In the end, it doesn't really matter, though. AMD's Fury X (which can be found for as low as $399 with a mail-in rebate) is beating the GTX 1070 (which is in stock for the low $400s) by a fair margin. The Fury X also beats its own OpenGL performance by up to 66% (at 1080p) with the new API.
The API should also make it easier for games to pace their frames, too, which should allow smoother animation at these higher rates. That said, we don't know for sure because we can't test that from just seeing FPS numbers. The gains are impressive from AMD, though.