Both of them aim to alleviate different issues but Mantle helps alleviate more issues in general and allows far bigger changes to occur in games.
more draw calls means more dynamic/unique objects in the game/on screen at one time allowing devs to create more unique, realistic and immersible environments with reduced cpu load freeing the cpu for other things.
fewer fps drops (even an increase in fps) and corruption issues as mantle runs bellow the normal windows api stack that directx has to call through before any calls are made to hardware
easier porting as mantle uses Microsofts HLSL as its basis so the majority of current DX code will most likely be a cut and paste job for immediate performance improvements before any to metal optimisation is performed due to Mantle being a thinner API.
better ports from consoles, as both consoles use GCN based hardware, even if sony and microsoft call their api's unique and only usable on their console, AMD still provides the hardware command lists their API's use so the code will most likely be very much the same and copy and paste for mantle ports for metal based code.
graphics card synchronisation will eliminate tearing and stuttering as stated which will be nice but still if the fps drops bellow a certain level (even 25 fps) it will look horrid still and does not improve performance in general. it would be nice if nvidia made it an open standard or if someone just done one up on nvidia and provided graphics card based synchronisation using displayport packets like nvidia is.
another big thing is AMD's true audio DSP, this will allow full positional 3d audio calculations using first order reflections of sounds using game geometry with direct access to the geometry info on the gpu allowing more realistic sound scapes and realistic sound effects to be generated in realtime.
amd did state that it can take 15% of a cpu to perform high quality reverb calculation (reverb being the sum of all the reflections for a given position in a space) but this is for a single sound of 5 seconds in length, most likely also including other modification of the sound due to surface texture type altering the reflected audio as with what aureal did with their 3d audio cards. (you can find some brilliant aureal 3d videos on youtube and here toni.org/a3d/)
the AMD sound DSP can process 100's of environmental sound calculations and effects with ease, even a high end xeon system would crawl to its knees as it is too general purpose compared to the DSP for this sort of workload compared to a cheap Programmable DSP.
we will just have to wait and see overall but im expecting mantle to give a large graphical and performance boost to new games on pc, we will get a demo of what mantle can do with basic implementation on the 11th as oxide studios will be showcasing its Nitrous engine using Galactic civilisation 3 as its demo game at AMD APU13 developer conference.