I've had some really weird results with Doom and my cards - my 780GHz had all kinds of issues with it in Open GL never mind Vulkan and my 1070 gets pretty much identical performance IIRC between Open GL and Vulkan but slightly different as in one will do better in some scenes than the other and vice versa.
My 780 was all over the place - 1080p performance was great and handled everything from low to ultra settings fine - turn it upto 1440p and performance took an utter dump regardless of low or ultra settings it was exactly the same poor framerate with no signs of being fillrate or VRAM limited and in Vulkan it would adhere to strange multipliers of the refresh rate like some kind of crazy V-Sync effect and only jump between like 30, 45, 60 and 120 fps :s (I think that was solved in later drivers but I was on the 1070 by then and haven't revisited it on the 780).
EDIT: Oh and some people saw a ~30% framerate increase on Kepler cards going to Vulkan for some reason but most didn't for no apparently reproducible reason either.
Yeah I'm pretty sure the Nvidia drivers are meant to be slightly odd with the new APIs. Not saying they're 'bad' but appears to be fair to say they don't perform exactly as expected, and consistently. The DX11 driver is clearly far more meticulously made.
Seems like only the GTX 1080/Ti/Titan gain in Vulkan consistently. And the weaker cards stay still, or lose very slightly. And also in DX12 Nvidia cards mostly lose mildly, or stay still.
Quite likely this won't be a problem with Volta, and when Vulkan/DX12 becomes more mainstream.
And Vega is supposedly fantastic for both too. Hopefully we'll see a lot of DX12/Vulkan games reviewed when RX Vega comes out.