I don't think I properly explained why 3GB of RAM for the OS on the XB1 vs. 1GB for the OS on the PS4, isn't really a big advantage for the XB1 when it comes to OS functions & Apps (besides the fact that Windows has a notorious reputation for being a RAM hog & slower compared to other OS').
First of all, like courtdog said: The Xbox1 has 3 OS's: 1 is the "Xbox OS" for gaming, 1 is "Windows 8" for The System OS/Apps. And a third OS made to assist both with interacting with each other...
The PS4's OS is called "
Orbis OS". It's a modified version of "
FreeBSD 9". "FreeBSD 9" free open-source Unix-Like OS, that is the base code for a lot of OS' like Netflix's Open Connect Appliance & Apple's "
Mac OS X". It'll be obviously used to run the games on the PS4.
The key thing to note is that the base "FreeBSD" has a built-in "
Linux compatibility layer". Since the PS4 has a x86-64 & a "
ARM" CPU, this means it's gonna be easy to port Apps/programs from Linux & Linux based-OS' (examples: Google Chrome/Chromium OS, Google Android, GoogleTV, Ubuntu, & etc.)
So the PS4's OS/Apps-capability is gonna be able to hold it's own against against the XB1, if not do better.
A little info:
PS4 News - Info on the Playstation 4 Operating System - The Orbis OS Based on Free BSD 9.0