DX 12 is said to vastly improve the Xbox One performance by vastly improving the graphics chip of the next gen console. DX 12 has a much lower level of abstraction and new rendering features and it also addresses state and features rendering overhead along with resource management improvements resulting in an overall better performance.
This has been confirmed by Phil Spencer on Twitter when he was asked, 'how beneficial will DX12 be for XB1 only?'
To which Phil Spencer replied: 'When you think about start of gen to end of gen teams learn a lot. DX12 will help as well, think PDZ to Halo 4.'
In fact that is totally true when you think in the entire lifespan of last generation consoles its only really the last year that those machines have been pushed to their limits. This isn't always down to the hardware or software of course, but also down to the game developers.
DX 12 will certainly help though with lower overheads, spreading the load over 4 cores, more efficient handling of graphics memory will all result in better graphics and smoother gameplay.