The way I see it is this: MS went for the sure thing to make sure they had 8gb of RAM. PS4 took a gamble on GDDR5 and the gamble paid off. Had the wager gone against them and the system wound up with only 4gb of GDDR5, then they'd have a better processor but be RAM limited, bringing (possible) parity more or less between the two consoles. But their GDDR5 bet paid off, so they wound up with just as big a pool (8gb) but with faster access speeds, and the better processor to boot.
Because of the (obvious) speed advantage of the GDDR5 over DDR3, MS needed SOMETHING to bridge the gap, so they opted for the eSRAM to help with that. I'm not saying they did this in reaction to Sony announcing 8gb of GDDR5, as it was probably already planned into the console design or we wouldn't see it releasing this year, as R&D time to change the core system structure would've prevented that if it were a last-minute addition since its on the same silicon as the APU. I'm just saying that they probably thought (and rightly so) that GDDR5 would at least be theoretical competition (even if a smaller pool had the PS4 wound up with 4gb instead of 8), and knowing it had faster access speeds the R&D department planned in the eSRAM to balance that out.
The unfortunate side-effect that adding on-die eSRAM had was that it reduced real estate for the processor. This resulted in a slower/weaker CPU and GPU in the XB1 vs the PS4. So while they may have brought the memory access speeds theoretically up to being on par with the GDDR5 in the PS4, they did so by sacrificing system compute and render power.
What I still don't get is why they couldn't switch to GDDR5 last minute anyway, but I suppose it probably has something to do with sourcing all that silicon, and it still wouldn't have fixed the problem of having R&D'd a system built around the eSRAM all along, a design choice with zero chance of being altered this late in the game (February 2013).
But rather than just admit this and move forward with "We're focusing on games, on innovative and fine-tuned gaming experiences for everyone. We want to fulfill the promises that motion gaming made to people and expand on that, to bring families together in the ways that a traditional power-centric console that isn't focused on innovation can" they are spinning PR bullshit that anyone with any sense can see right through.
I am NO fan of the Kinect. But that is the mast that they tied their flagship to, and by god if they're going to fall short in the power category then they need to focus on that. But they don't even have any jaw-dropping Kinect 2.0 experiences ready for launch. They're saying "We think our less powerful console is worth $100 more because we have this Kinect thing that we have no truly great software for yet, but yeah we promise it's coming". What they should be saying is "Here is our console for $350, and hey we've got these rad new things coming down the pipe with Kinect 2.0. If you want to get in on that action it will be $100-150", and launch the Kinect 2.0 once they actually HAVE a killer app for it.
Yes, I understand the chicken and egg scenario here. They need devs to support Kinect, so they need the install base, but if they don't even have anything ground breaking coming from FIRST PARTY studios for it, then why in god's name are they shoving it down our throats at a price premium? As much as I hate the Kinect I also realize that in the fight against the PS4's raw power, Kinect 2.0 really is their only trump card, yet MS 1st party studios have exactly zilch in the way of awesome games to showcase on it. The next iteration of Dance Studio and that Xbox One fitness thing are NOT going to sell anyone on the merits of the new Kinect.
I think this is the biggest factor against them when it comes to the whole console power debate. If the XB1 was launching at the same price as PS4 or even $50 less, people would still talk about it, but it wouldn't be as big a deal as paying 25% MORE for a console that is LESS powerful, and the price is all due to them bundling in an accessory that they aren't even bringing out any competitive software for.
I'm rambling now so I'll stop...