Stupid question, but where is the OS stored if it's not on the HDD? Is there flash storage somewhere in the system for it?
i think it's stored on the hard disk but the PS4 has a separate low power system included on the board
http://www.ifixit.com/Teardown/PlayStation+4+Teardown/19493
see step 20 in the tear-down
SCEI CXD90025G Secondary/Low Power Processor for Network Tasks
Samsung K4B2G1646E-BCK0 2Gb DDR3 SDRAM
Macronix MX25L25635FMI 256Mb Serial Flash Memory
by leaked architecture diagrams the low power processor is an multi core ARM design
i think the 32 Mb flash + 256mb ram is entirely dedicated to the downloading and networking,party voice, recording footage for sharing etc.
i don't know if the Xbox One has such a complete subsystem but they have a special processor for audio output and handling the HDMI input/codec stuff
edit: one has to be careful with the units here : that ram is Gigabit not Gigbyte in the teardown_ so those 2 Gb are actually 256 Megaybyte ram and the flash memory ist 32 Megabyte
sorry for the mistake