It's a good question
The main advantage is that the version without normals uses significantly less memory. There are two reasons for this:
1) We have less data per vertex, in that we have 3 position components rather than 3 position components + 3 normal components. This is the obvious saving of a factor of two.
2) The less obvious (but actually more important) saving is that we have less vertices. Typically we would expect a cube to have 8 vertices, and we would expect these to be shared between adjacent faces. The problem here is that all the adjacent faces actually have completly different normals. As a result, vertices do not get shared and you end up with 24 vertices for a single cube. In this case it's a factor of three differnce, but actual result will depend on the shape of your volume.
As AndiNo says, you can choose which ever one is most appropriate for you. In another post you also mentioned Minecraft and per-vertex lighting, if you want to use this then you will need normals in you vertex shader and in that case you can't use the ddx/ddy approach.