The common misconception seems to be that Mantle brings only CPU gains, and only helps with low end GPUs. This is not true.
Here are some examples of potential GPU gains:
Bindless textures and hardware virtual memory (*) allow rendering in larger batches, thus increasing the GPU utilization (GPU partially idles at start/end of draw/dispatch calls). Application controlled memory management means that GPU needs to shuffle less resources around (this isn't only a CPU hit and many current games have frame rate spikes because of this issue). Also the developer can pack resources more tightly (multiple resources in same page/line, increasing memory/cache utilization). With Mantle you can run multiple kernels in parallel (or kernel + graphics in parallel) in a controlled way, and thus reduce the GPU bottlenecks. For example render a shadow map (mostly ROP and geometry setup) and compute ALU heavy pass (for example lighting for the previous light source) at the same time. This results in much higher GPU utilization. Better predicates and storing GPU query results to GPU buffers (without CPU intervention) allow GPU optimization techniques that are not possible with PC DirectX. AMD also claims improvements to indirect draw/dispatch mechanisms, but do not spill the details in Mantle slides (these improvements potentially bring big GPU gains for certain advanced use cases). Direct access to MSAA data could also make deferred rendering AA much faster (more about that in the reply below).
(*) DirectX 11.2 also has partial support for hardware virtual memory (in form of tiled resources). However it has limitations and the Windows 8.1 requirement basically makes the API useless right now (Mantle has much bigger user base right now). Hopefully Microsoft will solve this issue, and bring some other Mantle's features to 11.3 (and/or 12.0).
AMD announced that with Mantle we finally have full manual access to both GPUs in Crossfire. This is excellent news. I was quite worried that SLI/Crossfire would die soon, as many new graphics engines will start doing scene management and rendering decisions on GPU side. Alternate frame rendering (with automatically synchronized memory between cards) is just not a good fit for a scenario where the data set is mutated slightly every frame (by compute shader passes that are pretty much impossible to analyze by automatic logic). AFR works best when everything is freshly generated during a single frame and there are no dependencies to existing data. However this kind of processing is a huge waste of GPU (and CPU) time, and frankly we can do much better (and I believe that forthcoming "pure" DX11+ engines that have no legacy baggage surely will). With Mantle, supporting Crossfire is possible even in these kinds of advanced GPU driven rendering engines. Hopefully Nvidia releases something similar in the future as well, or they will see very bad SLI scaling in some games/engines in the future.
Deferred antialiasing will be much more efficient, assuming the "Advanced MSAA features" in the Mantle slides means that you have direct access to GPU color/depth blocks and MSAA/layer data (including coverage sample index data). With all that data available, tiled (and clustered) deferred renderers can separate pixels (different sample counts) more efficiently and recover geometry edge information (using coverage samples) in a much more precise and efficient way.
That would definitely give a big GPU boost for a deferred renderer with MSAA (especially with coverage based EQAA/CSAA). Of course estimating the gains is not possible right now, since AMD hasn't yet released full Mantle API specifications, so we don't know exactly how low level access you have to the MSAA & depth/color compression data.