That gets back to Sony's "gaming first" strategy that I mentioned earlier.
Even back in 2010-2011, when MS started designing the XBone and Sony started much earlier the only way to guarantee 8GB of RAM was to go with DDR3. DDR3 doesn't meet the performance requirements of modern GPUs, so going with DDR3 meant needing a high-speed "cache" to try to keep the GPU fed, hence the eSRAM. In turn, the eSRAM takes up tons of space on the die, meaning the GPU portion needed to be shrunk to accommodate it.
All of that would have the effect of reducing gaming performance, so to Sony, it wasn't really an option. A powerful GPU and 3.5GB of high-speed RAM to feed it made for a better gaming machine than a weaker GPU and 5GB of RAM that can't even keep up with the gimped GPU, so that's what they did. Gaming first.
Where Sony got lucky is that at the last minute, GDDR5 did jump to 8GB, allowing Sony to increase the game dev's RAM allocation from 8xPS3 to 11xPS3 (or more), while also bumping the OS allotment to 6x what they had originally planned.
If GDDR5 hadn't made the leap, Sony would've been "stuck" with the console that offered the best possible gaming experience, and not a whole lot else. As it stands, that's given them the console with the best possible gaming experience and the ability to do a bunch of other stuff at the same time., though a lot of that extra functionality will be coming in the future, as 8GB really did come at the last minute, and they really haven't had much time to make use of it
Yup. The way XB1/PS4 ended up relates directly to the priorities of each platform holder.
MS: Wanted a multimedia box with Kinect -> 8gb needs to be there -> Only way to guarantee this early in the development cycle is to use DDR3 -> Too slow, need ESRAM on chip -> Weaker APU as a result -> More complex system to dev for and similar BOM as PS4 (sans Kinect).
Sony: Wanted the best games box -> GDDR5 is the best ram to feed GPU -> Can only use 2-4gb of it early in the development cycle -> XB1 has 8gb, we need to tighten our belts and make 8gb GDDR5 happen -> Good APU, no need to spend die space on embedded ram -> Easy to dev for console with similar BOM as XB1.