DX12 and other modern graphical APIs (Mantle, glNext / Vulkan) achieve performance boosts by moving as much stuff out of the CPU and into the GPU, lowering the amount of memory copies, multicore support, and reducing bottlenecks caused by synchronous / single threaded locks.
Kind of nebulous to say 20% improvement (or 100% as previously claimed) because it probably means with specific use cases.
Given how similar the PS4 and XB1 are, anything that one can do can probably be replicated by the other. I expect Sony, Valve and others will get behind Vulkan which will deliver similar gains in a more cross platform fashion. Given that DX12 is only appearing in Windows 10 / XB1 and Vulkan god knows when, it'll probably be a few years before either of them is especially prevalent.