The first game to use DX12 is Ashes of the Singularity an RTS based game. Testing shows that DX12 does improve performance although it varies depending on choice of card:
Dx12 runs far better on the AMD cards than Dx11 does so they will see the most benefit in this instance. Other games (depending who's backing them) may show different results. Read the article here.
As evident in the charts below, gamers with AMD graphics cards in particular are in for a massive performance improvement. Less so on NVIDIA cards as they performed better on DX11 to begin with, resulting in much smaller gains with DX12.
Dx12 runs far better on the AMD cards than Dx11 does so they will see the most benefit in this instance. Other games (depending who's backing them) may show different results. Read the article here.