While the eDRAM gives the 360 tangible advantages over the PS3 (its the reason why so many cross-format titles have anti-aliasing on 360 while it is omitted on the PS3 versions), 10Mb isnt really enough for a full 720p framebuffer with the added overhead of anti-aliasing. Instead, developers switch memory in and out of the eDRAM in a process called tiling. This incurs an increased geometry cost for polygons that span more than one tile. In plain English? Realistically we expect the 360 version to match the 720p and 2x multisampling anti-aliasing of the PS3 game, but at a cost the HDR lighting in the PS3 game will most likely be pared down from high range to medium range dynamic rendering.
Few games on 360 run with proper HDR. Halo 3 is one of them, but this comes at a cost of a sub-HD resolution and no anti-aliasing. In the case of Final Fantasy XIII, the drop down to MDR simply makes more sense as opposed to savagely cutting down resolution or anti-aliasing. So aside from small changes to lighting, we expect the games to be totally like for like in the real time 3D sections, and due to that lightning fast eDRAM, theres a strong chance that performance may actually be smoother. How small will the changes to lighting be? Considering we spent the best part of the day firing off 'is it proper HDR/isnt it' emails to one-another, lets just say that its highly unlikely any one will notice. A useful by-product of moving away from proper HDR on 360 will be that the alpha transparency issues the PS3 version has with the way it handles characters hair will most likely vanish.