In and of itself, since it has to be written for both AMD and Nvidia product, it might not be an extreme boost like Mantle can in some games, since Mantle is primarily written for and beneficial to AMD hardware architecture, but there are many ways an API can be made universally more efficient, just by minimizing how many commands, esp unnecessary repeat commands, are asked of the hardware.
Pascal is the architecture that's really going to take it to the next level by incorporating stacked DRAM, unified memory, and NVLink into the architecture. I'm sure AMD as well are working on architecture changes of their own to prepare for Dx12, but while they were working on Mantle and Crossfire, it was Nvidia that was collaborating on Dx12 with MS.
You can draw your own conclusions from that as to whom will have better (if at all) DX12 support going forward, but it's looking like Nvidia may have the edge at it's launch.