PlayStation 4 is incredibly small. It may be hard to tell in photos, but the hardware is tiny. Official specs released by Sony show that PS4 is closer in size to the PS3 Slim than Sony's launch PS3.
Unfortunately, Microsoft has not released concrete numbers on Xbox One, leaving it to internet sleuths to attempt extrapolating that data based on official photos and measuring USB ports (which should be the same size on every device). This photo (via CVG) has been making the rounds, highlighting that Xbox One has a larger footprint than PS4.
The hard-to-see disc drive of PS4 does call into question doubts over the accuracy of the image. However, NeoGAF members seem to agree that this is the real deal. The forum also notes that while Xbox One still has an external power source (aka "power brick"), PS4 does not.
However, because of the way the image is constructed, the Xbox One comes off as much larger than it actually is. While PS4 is smaller in volume and width, this image shows that PS4 is actually longer than Xbox One. Still, given the way you'll likely position these systems in your living room, this comparison is still apt.