While we wait for Vulkan and DirectX 12 to gather momentum, developers are still tweaking the knobs of DirectX 11. The team behind DayZ for example are currently putting the finishing touches on the game's "Enfusion" rendering engine, which is powered by older API.
The technology isn't quite ready for prime-time it seems, but Brian Hicks, DayZ's creative director, was happy to show off the differences between the new renderer and the current DirectX 9 renderer in the video above.
It's interesting, though I reckon Hicks spends way too much time running around a completely dark scene, which doesn't really provide a good comparison. However, from about the 5:30-mark, we get to see a geometry-heavy area where the performance boost is significant — usually in the order of 1.5x to 2x, and sometimes better.
You might be wondering why the developers are bothering with DirectX 11 instead of 12 (or even Vulkan). The long and short of it is that 11 is a tried-and-true API that's fully supported on all modern hardware — and a great deal of GPUs from even five years ago. So the benefits will be felt immediately by the majority of users once the update rolls out.
.60 Dev Log / Performance Comparison [YouTube]