The first DirectX 12 benchmarks are in, and they bode well for the new API.
With a little help from Microsoft and Oxide Games—not to mention AMD and Nvidia—Ryan Smith at AnandTech was able to test a DirectX 12 version of Oxide's Star Swarm benchmark. The results show that DX12's lower-level hardware abstraction layer already improves performance and cuts CPU overhead dramatically.
According to Smith's numbers, Star Swarm's DirectX 12 and Mantle code paths are about neck and neck on Radeon cards, with Mantle offering a slight performance edge. GeForces also see substantial benefits from DirectX 12, though the improvement over DX11 is smaller on those cards, since they seem to handle Star Swarm's DX11 code path a fair bit better than the Radeons.
Also interesting are Smith's CPU scaling tests, which show that, for the most part, DirectX 12 allows Star Swarm to run just as well on dual-core processors as on quad-core ones. The only exception is when a GeForce GTX 980 is used, in which case four CPU cores are better than two.
Smith's article includes plenty of other interesting data, including power consumption and frame-time numbers, so you'll want to check the full review for all the details.
Just keep in mind that DirectX 12 is still a work in progress—Smith says the current software is "pre-beta"—and that Star Swarm is kind of an idealized showcase for the benefits of low-overhead graphics APIs. The benchmark can churn out more than 100,000 draw calls per frame, which is a couple orders of magnitude more than what current games are limited to.
For more info about DirectX 12, don't miss my writeup from last year's Game Developers Conference.