Now that all of the pieces are finished, it looks like red oak turned out the best (upper left in the picture below), followed by mahogany (upper right), then walnut (lower left), then maple (lower right) respectively. By best I mean they had more detail, and less thick, deep burns. This is subjective of course, and other people might be looking for a different effect.
My hypothesis was that the harder the wood, the more detail would show up, and the softer the wood, the deeper and thicker the burn would be. While this seems to be generally true (pine and MDF burn thicker and deeper with less detail than hardwoods), between hardwoods there seems to be other factors effecting the pattern. Confirming my theory, Red Oak is the hardest of the woods I tested, and it did have the most detail. Maple is the softest, consequently having the least detail. Walnut, however, is harder than the Mahogany by a significant degree, but it burned decisively deeper lines with less detail than the Mahogany. Further experimentation along with additional research into the characteristics of the woods will be necessary to determine what factors other than hardness effect the burn patterns on various species of wood.
Now that the experiment is over, and the Lichtenberg machine has been relegated to it's spot on the shelf, I am once again left with a bunch of wood panels with neat designs but no real purpose. This time I decided to do something with them. I was not overly impressed with the Maple, so I set it aside and proceeded to finish the other panels with four coats of polyurethane. With some brass hooks and eyelets, and a length of brass chain, I connected the panels together to create a simple wall hanging. I think it turned out nicely.