I now have both the Black and White Nexus 5's in house, and well there are actually some differences. Of course, from YouTube noticed most of these differences first, so props to him. After using both for a few hours now, I've noticed that there are quite a few differences too. Not just the color. Let's start out with the front of the device.
On the front of the device, the earpiece is white on the white Nexus 5, while stays black on the black Nexus 5. On the sides, you'll notice that the white Nexus 5 actually has a glossy side like you'll see on the front of the device. While the black one is the same soft material that's on the back. So naturally, the black Nexus 5 has a bit more plastic to peel off as the white one has plastic on the sides to peel off as well as the front, while the black one does not. Now on the back, yeah there's not much there. The White one is white on the back and the black one is black on the back. Surprising right? But that's not where I'm going here. The black Nexus 5 is a bit more sensitive to fingerprints than the white one. I'm guessing because it's a darker color than the white one. Not a huge deal though.
Onto the box. Many of us probably won't notice this. But the Black Nexus 5's box just shows the black phone. While the white one shows two phones. One straight on, and the other is the side of the phone. On the back of the box you'll see the back of the black phone, of course on the black Nexus 5, and for the white Nexus 5, it'll have the back of that one there.
So there's some very subtle differences between the two, and if you've never seen both of them together, you'd probably never even notice the differences, but they are there.