In fact the HD 7770 has the same amount of main bandwidth than the Xbox One, even while using GDDR5, cause X1 has a 256-bit bus and the reference card have a 128-bit bus. They ve chosen to put a wider bus to be able to use cheaper ram. A 128 bit bus like the HD 7770/7790 would be terrible with DDR3 (about 35 GB/s). Hopefully they didn't do that.

Btw, Having more bandwidth is always a good thing, even if you have less raw power, input bandwidth is most of the time the first bottleneck in real time rendering. Then i would say, in my experience, fillrate is also very important. PS4 have 100% more fillrate due to  the 32 ROPs (16 on X1)

Really, the main reasons for DDR3 are:

1) Lower BOM cost (yes I know it is more expensive than PS4 but that is NOT due to RAM cost)

2) Latency for media function, where the Xbox might show a slight advantage..

Not going to lie.  I envisioned this happening and lol'ed.

That's not how it works. Xbox One would benefit greatly from having GDDR5 RAM as the huge ESRAM chip wouldn't be necessary and it would even lead to a slimmer form factor. Then there's the obvious advantages of having more bandwidth and having faster access to it. It would also make porting between PS4 even easier.

Microsoft chose DDR3 because its what was available 2 years ago when they chose their specs. If they were more forward thinking and pro-active in developing technologies, they could have easily matched the PS4.

If I'm not wrong, wouldn't GDDR5 RAM allow for faster loading of apps and just more graphically intensive apps in general? This is a much better advantage than shaving 2 seconds of latency between app switching.

If you're suggesting that the RAM will not be the bottle neck since the GPU is what it is, then yes and no.  GDDR5 is still a better video ram (equally big textures for both systems, big (slower reacting) pipe).  But DDR3 latency does have advantages for the media functions (switching, etc.) that Microsoft prides themselves on.

 I'm not arguing with you, I'm just saying its not exactly black and white in either direction.

There s no latency advantage with DDR3, it's a myth. In fact GDDR5 has better latency, it's just better memory chip s who can handle a higher multiplier, the main difference between the two type of memory, is with DDR3 you multiply the base clock by 2 and 4 with GDDR5. GDDR5 base clock is also higher.

It's simple math

XB1 = 1066 x 2 x 256 / 8 = 68 GB/s
PS4 = 1375 x 4 x 256 / 8 = 176 GB/s

MS always wanted 8GB but GDDR5 was not available to that amount when they designed the Xbone project... so the only alternative for MS was use DDR3 with eSRAM to avoid the possible bottlenecks.

They are paying for that decision with yields issues created by a big, complex and expensive APU.

I'm sure if at time of project the GDDR5 was available to 8GB then MS may use GDDR5 instead DDR3... they used GDDR3 for 360.

So to reply your assuptions in OP... MS needed GDDR5... without it they have to go in another path not easy.

PS. Why did you try harder to defend the bad MS decisions?

No... both have rediculously fast memory that you will not see any loading benefits for apps. 

Also Xbox one will have less latency due to different RAM.

Think of it this way...If this was a burger eating contest, PS4 can take larget bites but Xbox One can take smaller bites more often. So for multitasking Xbox one would win since there is less latency between RAM reads. 

Only with GPU processing of high end visuals will there be a difference thanks to the more powerful GPU in PS4 and its faster memory bandwitdh thanks to GDDR5 RAM.

PS4 can not only take larger bites but it also has a bigger stomach.

Define "win". How much faster would it be? Milliseconds? Is it worth it? How often will people really be switching between apps? IMO, the advantages of DDR3, whatever they may be, aren't worth it.

Qft... The cloud will be the more problematic issue this gen. Other than using it for saving data it could become more difficult than its worth. One thing is giving up server control to ms, and who knows what kind of hoops 3rd paryies will have to jimp yhrough to update it, might be painless might not. Also server side applications might be a lot challenging to set up for a game to run properly on and off the cloud.