I would not expect MS to be down-and-out ala Sega (or Nintendo) as of both systems being cut from the same (AMD) cloth with a Benjamin of a price difference between them.
Remember as of devs pushing MS hard to give the launched 360 the same amount of RAM as the devkits at the time, they where at the mercy of graphics ram (GDDR3 [http://en.wikipedia.org/wiki/GDDR3]) manufacturing capacity, and that severely limited the number of systems MS could put on store shelves at the end of '06 and much of '07. Sony may be in the same boat now: no one outside of boutique workstation add-in-board makers are requesting a dual-layer DVD's worth (8 billion* bytes, aka 8 gigabytes) of primary graphics memory (GDDR5 [http://en.wikipedia.org/wiki/GDDR5]) per device right now. Meanwhile there is a glut in the desktop computer memory (Double Date Rate 3 [http://en.wikipedia.org/wiki/DDR3_SDRAM]) market, and the Xbox One uses (aggressively clocked) ordinary desktop memory.
Likewise Microsoft is simply in a much, much better financial position than Sony, and may well out-manufacture [http://www.forbes.com/sites/erikkain/2013/07/23/analysts-says-xbox-one-could-outship-ps4-3-to-1-at-launch/] Sony.
Unlike the relatively few folks like us (or Carmack) who follows this stuff, Joe-Public seems to have far less of an aversion to the Kinect, as it is the best selling (and was the fastest selling) console peripheral to date, so the larger inventory of One at and past launch may have no problem flying off shelves despite Microsoft's $100 price handicap. It'll get bought because it's there, while the PS4 is simply unavailable for days if not weeks at a time.
[sub]*like a baker's dozen, JEDEC's billion is different from your billion. Theirs is 1024*1024*1024 (2^30)[/sub]