It is still a bit too early to tell who will have the upper hand in DirectX 12. Recently there was quite some controversy about the performance of NVIDIA's cards in Ashes of the Singularity, resulting in speculation that perhaps DX12 would level the playing field and give AMD a better chance to get the upper hand. Once NVIDIA enables proper Async Compute driver support and more DX12 benchmarks arrive we'll get a clearer picture of the situation.
At least for now, AMD is claiming victory and Robet Hallock, the Head of Global Technical Marketing at AMD, claims the vast majority of DX12 titles launching in 2015/2016 are partnering with AMD:
“You will find that the vast majority of DX12 titles in 2015/2016 are partnering with AMD. Mantle taught the development world how to work with a low-level API, the consoles use AMD and low-level APIs, and now those seeds are bearing fruit.”
So far little has been revealed about which major DX12 titles that are partnering with AMD, apart from Deus Ex Mankind Divided and Ashes of the Singularity.