I think the PS4 and PC versions will support mantle due to PC being flexible with both DX and Mantle. Plus the PS4 uses AMD hardware so it would make sense for it to support it while Microsoft will use DX12 for the XB1 as it's their territory.
I would like to point out a few things, while both new consoles use AMD hardware, and DirectX 12 is coming to Xbox One, it will not be the same as the PC version, because it sort of defeats the point as to why API's such as DirectX were made in the first place. DirectX 12 on XB one will be aimed more at ease of portability for games, and graphical features rather than performance because consoles developers by the very nature of consoles have a much lower level access to the hardware, than that of PC.
DirectX was made so that game developers could make games relatively easily for PC, given the thousands of different hardware configurations out there, it would take forever to game developers to write the code to make their games run for this massive amount of hardware configurations, DirectX took all this hard work out, and enabled developers to write code for DirectX. In theory, their code, or game would then run on any hardware configuration that supported DirectX, with relative ease. Microsoft took care of making sure DX would run on a massive amount of different hardware configurations, and then all the developer needed to do was make sure their game would run on DirectX.
Consoles do not, and never have had this problem, because every console line has exactly the same hardware configuration. This means developers do not have to mess about with computer resource sapping API's and also means not only do console developers get more efficient use of the hardware, they also have a more direct and lower level and much faster access to the computer hardware, this was the case 10/15 years ago, and is still the case now.
If you had a PC with the same specs as an Xbox 360, would it run GTA IV, let alone V? No, it would not, in fact it would not even be close. One of the main reasons why it can be run on such slow hardware when compared with a PC is because the developers do not have to mess around with API's that are as complex as PC API's because the do not need to. This massively makes code and thus games run much much faster.
If Mantle however comes to GTA V, systems that are CPU limited should almost certainly see a performance increase when using Mantle as appose to DirectX, I posted a more detailed explanation as to why this would be the case in the 'Nvidia or AMD for GTA V' topic on this sub forum,