I recall reading somewhere about MS deciding from the start that they wanted 8 GB of RAM in the system, but decided against using GDDR5 because the price was (at the time) too high to make it work, hence using 32 MB of eSRAM to make up for the memory bandwidth deficit. As for the weaker GPU, I'm guessing it is likely due to a combination of cost reduction (bundling in the Kinect leaves less room/$$$ for the console itself) and how MS wanted to market their console, i.e. home entertainment box first, gaming box second => less need for a powerful GPU.
As for Sony, I recall they originally specced the PS4 with 4 GB of GDDR5, chosen because it is a hassle-free means of providing the GPU enough bandwidth. As for the reason behind why the PS4 now has 8 GB of GDDR5, it was because the prices for GDDR5 had come down faster than they anticipated, so they upped it to 8 GB. Sort of a ballsy move from Sony that ended up paying off in the end.