Well if it comes to BF4 you proberbly want to have a 7000 series card or newer.
The new Mantle update that comes ot in December is not going to make a few procent difference.
But more likely 10 to 50 procent difference.

The idea behind that is basicly stolen from consoles where they need low level hardware acces to make sure games can run on it due to the fact that consoles pack a lot less powerfull hardware.

Now they make low level hardware access available on pc so BF4 with manta is going to take 100% advatnage of your hardware where directx is not cable of doing so.

That has a reason, directx needs to be multi multi multi multi compatible with all software/hardware you can find on this planet. So it is inefficient as it can be because of that.

Mantle is working with whatever developer is going to use that api and the hardware that supports it.

It is going to be open source but i think amd made the decision to release it in December. Guess what that is the month they will sell shitloads of stuff and nvidia is not going to release anything qiuckly after that because they need time to make it work on nvidia cards.