When you visualize the next-gen consoles in your head, you don't think about a huge size discrepancy between them. But, there is, and it's big. You can see the difference in the pictures below.
The Xbox One is quite a bit bigger than the PS4, but why? The PS4 is the faster console overall, so what is Microsoft's excuse for the Xbox One being so big? Maybe it's cooling system is superior to that of the PlayStation 4, maybe.