I think Microsoft's design decisions are pretty straightforward. I wouldn't say it's "backwards" per se, but more holistic in terms of competing goals for the hardware.
1) Power was not the only goal of the console - OS features, Kinect, and gaming all had priorities when designing the console, so 8GB of RAM was a must in order to ensure enough memory resources.
2) The console was going to pack-in Kinect as standard. This required more robust audio hardware, it would also increase the cost of the console. As a result, other components needed to be cheaper in order to keep costs down.
3) In order to meet the goals of 1) and 2), a single APU design was necessary in order to decrease costs and allow die shrinks to continue decreasing costs significantly over time. 8GB of RAM was also a requirement, but it needed to be a cheap solution that could be targeted for 2013 release -- thus 8GB of DDR3 was chosen.
4) In order for 8GB of DDR3 RAM to be able to hold up in 2013, a secondary pool of high speed memory was necessary - thus, the decision could have been eDRAM or eSRAM. The latter was ultimately chosen because it could be integrated with the APU.
Microsoft went into the design of Xbox One with the mindset that all of these factors needed to be met. GDDR5 may have increased the BOM more than they would have liked, and it also may have not been guaranteed for 2013 release (remember Xbox One was designed two years ago).
Sony went into the design with a different philosophy; instead of competing interests for OS functionality or Move, they decided to focus designing the hardware around games and developers first, and then whatever resources they had left over would be allocated to either of these functions but they were considered of secondary importance.
It's why Sony was originally willing to go with 4GB of GDDR5 -- sufficient for gaming purposes, and in many ways still superior to the 8GB of DDR3 purely for rendering. It would have required a smaller OS footprint for the PS4, so Sony was conceding at that point in time that they may have not had the ability or memory resources for all the advanced multi-tasking that the Xbox One is capable of. Bottom line is that 8GB of RAM was never a requirement from the outset of the project design. This allowed Sony to focus the APU purely around providing the best GPU bang for their buck -- they picked a highly customized Pitcairn GPU with advanced GPGPU functionality coupled with a relatively modest CPU.
So Sony was giving developers what they wanted the most out of a next-gen consoles -- RAM bandwidth and a powerful GPU. It just so happened that they lucked out and 8GB of GDDR5 became available in 2013, further removing developer limitations with the console.
Sony and Microsoft had two very different philosophies for next-gen, and I think they were entirely based upon their experiences this gen. In the case of Sony, many people felt PS3's design was overly complex and the cost was too high due to Blu-Ray and CELL, while the memory architecture was causing developer headaches. It left Sony fighting to win back the core audience they had been losing to Microsoft. So their PS4 design was based upon winning them back.
Microsoft in comparison, felt pretty confident that they had the hardcore gaming audience in the bag, so to speak. And they had been riding high off some relative success of an expanding userbase thanks to Kinect. So they doubled down on this strategy, and focused more on expanding services.
Hence why we have the two systems that we have today.