"Because the normal at each pixel in a normal map is completely independent from its neighboring normals, normal maps can produce effects not possible with bump maps, while still being able to do everything that can be done with bump maps."

Agreed, and this is also why the above pix is an 'Apples and Oranges' comparison anyway... Normal maps work best when they are extracted from high rez meshes and used to duplicate that detail on low rez ones. For this, they are far superior to bumps as bumps are limited to small perturbations of existing surface normals only. You can't, for example, take the normals of a sphere and put them on a cube with bumps, whereas this is perfectly possible with normal maps. And normal maps are indeed faster as they only involve simple addition of vectors, while bump maps require a differentiation which is a much more expensive calculation. But of course this is poser, so god only knows what the heck is being done to them to make them slow like that.

Also note that while you can't increase the depth of a normal map, you can reduce it by weighting against a neutral vector. But generally it is better to make your changes to the sculpt itself, cause this way all you other maps remain consistent.