It looks like English walnut (Juglans regia) is the tree that produces the walnuts you'd get in the supermarket. Does black walnut (J. nigra) produce nuts that are worth eating?
Are there varieties of either species (or perhaps other walnut species) that have some quality to recommend them over other varieties?
No. The nuts produced by Juglans regia and its cultivars have the thinnest shells and the largest kernels. Black walnut (J. nigra) does produce nuts, but they are much more difficult to extract from the shell. There are cultivars of J. regia which may be chosen by professional growers for various reasons - perhaps the growth habit is broader and less tall, or flowering is later to avoid frost damage in regions where spring is late. Bear in mind these trees are best grown separately - the roots have an allelopathic effect, particularly J. regia roots, and may kill off surrounding planting, although some plants are more suspceptible than others to the toxin. You may also need more than one tree to guarantee fruiting - although they are self fertile, carrying both male and female flowers on a single tree, sometimes they appear at different times, so that fertilisation cannot take place.
