Yes and no, you've got it a bit confused. Normal maps and displacement maps are entirely different things, therefore you can't really say that one is superior to the other.
ZBrush doesn't use any sort of map, other than the psd's or jpeg's that are its brush files. What it does, is to give you the option to export your sculpt in the form of either a displacement or a normal map. And as I mentioned, normal maps are a more sophisticated version of bump maps, while displacement maps offer the ability to render real volume using b&w images.
Poser supports both as far as I've seen. I'm not very sure about Pro, but I've seen that 8 does have options regarding normal maps.