It's a bit hard to tell since Youtube render quality gets in the way and the side-by-side comparison is of gameplay that is close, but not identical. That each is different is a little distracting, frankly.
After hearing how DirectX squeezed competing technologies out of the market, I'd very much like to see something grow in spite of it, and as a regular Linux user, even better.
The quality is same as are the settings. The thing you need to look at is the small FPS number in the upper right corner, and it shows that on vulkan in runs for 20 fps less.
Here is more detail testing and it looks not that good, it performance is somewhere even worse compared to older opengl in some tests, and direct x11 blows it out of the water, but also to note is that the devs didnt fully optimize the game for vulkan.
http://www.anandtech.com/show/10047/quick-look-vulkan-performance-on-the-talos-principleDX12 will definitely be the API Vulkan has to truly compete with to survive, but we can't compare the two because there aren't any games/demos that run both Vulkan and Dx12. In fact, are there even any dx12 games out yet?
Incidentally, how did it compare to DX11 in the video? I've not watched it because I'm on mobile.
There are or better said is, Ashes of Singularity and they tested directx11 vs directx12
https://www.youtube.com/watch?v=baBSqY-U7VUIn short there is a increase on average of 20% to 30% better performance, or from 10 to 20 more fps.
There is also Quantum Break a first directx12 only game that will work only on windows 10 that will be released this year I think. But it system specs are probably the highest ever for a game I saw(edit: they mixed up recommended with ultra so its not as high as it was):
Minimum:
OS: Windows 10 (64-bit)
CPU: Intel Core i5-4460, 2.70GHz or AMD FX-6300
GPU: NVIDIA GeForce GTX 760 or AMD Radeon R7 260x
RAM: 8 GB
VRAM: 2 GB
HDD: 55 GB available space
DX: DirectX 12
Recommended:
OS: Windows 10 (64-bit)
CPU: Intel Core i5 4690, 3.9GHz or AMD equivalent
GPU: NVIDIA GeForce GTX 970 or AMD Radeon R9 390
RAM: 16 GB
VRAM: 4 GB
HDD: 55 GB available space
DX: DirectX 12
Ultra:
OS: Windows 10 (64-bit)
CPU: Intel Core i7 4790, 4GHz or AMD equivalent
GPU: NVIDIA GeForce 980 Ti or AMD Radeon R9 Fury X
RAM: 16 GB
VRAM: 6 GB
HDD: 55 GB available space
DX: DirectX 12