Minor correction, apropos nothing, but a black and white (B-W) bump map is 1-D, not 2-D. Black and white are the two ends of the only dimension it records. RGB has three black and white maps in it.

The chief performance advantage of a normal map, as the OP pointed out, is speed. The delta to the normal is directly available from a normal map. From a bump map, the delta to the normal must be derived by computing gradients from neighboring pixels. In Poser, this speed advantage is unmeasurable.

The chief usability advantage of a normal map, as Fugazi pointed out, is that the perceived depth is always the same, and cannot be screwed up by the user. For example, if every V4 texture came with normal maps instead of bump maps, nobody would ever get the advice "I think you have the bump set too high."

If you're not starting with the premise of some known geometry being simulated, then the notion that the depth is fixed is actually not an advantage. It's a flaw. If I want to re-purpose a bump map to make an object appear more or less bumpy, I have the simple freedom to change the bump depth. Not so with normal maps.

For procedural shader work, a bump map is far more flexible. I can read the height out of a bump map and use that info to drive other things, such as color or shine. The most common and familiar use case is ceramic tile. A bump map for that tells me whether I'm drawing the tile or the grout and can be directly deployed in a Blender node. The normal map version of the same surface is unusable for this purpose, since both the tile and the grout have places where the normal is unchanged, i.e. pointing straight. Thus they have the same data and are indistinguishable.

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)