Both PS4 and the next Xbox are based on the same identical AMD APU technology.
All the differences so far depend on a single element: the memory system.
Microsoft wanted to have a lot of memory capacity for their non gaming ambitions and in the design stage they thought they could only achieve that with DDR3. Sony initially settled with a lower capacity thinking that bandwidth was more important for games and 4GB was enough so they designed the system around GDDR5.
To overcome the bandwidth limitations of DDR3 while keeping the die size of the APU the same, Microsoft had to swap a few compute units and ROPs in the GPU for 32MB of embedded memory.
For all the other purposes it's absolutely realistic to think that AMD is providing the same APU.
Honestly I think that Microsoft might be a bit angry and frustrated internally at the moment for the fact that right at the last minute thanks to the introduction of 4Gbit GDDR5 modules, 8 GB of GDRR5 have become feasible at a reasonable cost, so this fact has a bit invalidated their design approach.
But at this stage there's nothing they can do if they want to release their product in 2013, still they'll enjoy a cheaper BOM because of DDR3 vs GDDDR5 and that could offset the financial burden of the inclusion of Kinect 2 in every console.