At 1080p I think you're going to run into bottlenecks besides memory usage with a 670 or 270X. I've been pretty satisfied with my 270X so far, with MSAA turned off of course. Have you been playing the game with your 670?
I've been trying to, it's a stuttering, hitching mess. From what I've read windows 8.1 would clean it up quite a bit with an NVIDIA card, but mantle will help much more, especially once the mantle memory leak is fixed.
I think the draw call improvments are universal, can you link to anything specific for 11.2?
The 280x should be fine and you'll have the advantage of Mantle. You may have to turn MSAA off but the shader based AA is pretty good and doesn't blur things. Some people turn the tessellation distance setting down for a bit of extra performance but I like it maxed.
http://www.hardocp.com/article/2013/11/24/battlefield_4_windows_7_vs_81_performance_review/5
http://www.guru3d.com/news-story/battlefield-4-gets-dx11-1-dx11-1-will-improve-cpu-performance.html
I'm not 100% sure that draw calls weren't improved in W7, but the features used to improve BF4/Frostbite did not make their way into windows 7.