The worlds Jordan and Tolkien have created are built out of the ordinary atop a substrate of extraordinary. I'd like to look at the invisible forces first, that is, how their worlds are constructed and the forces, technological and magical, that manipulate each one.
Both Jordan and Tolkien have an implicit direction of technological advancement. This is obvious in Jordan, with characters who invent cannons, gunpowder, and steam engines. I like those details, it gives the books a steampunk vibe that is different from Tolkien's vision. True, Jordan's visions of the distant past include flying vehicles and other futuristic images, but it's never clear if those are magic or science (or, in Clarke's famous quote, both?). Whatever happened in the Age of Legends, for the current age, science and mechanism is providing a way forward.
What most people don't realize is that Tolkien has a more tragic, less mechanical vision of progress, but he has a vision nonetheless. Although he's vague on these points, Tolkien at times told others he intended Lord of the Rings to be our own myth, in our own past. As such, it shows the ascent of man and the departure of the elves. The dwarves, ents, and even the Astari/wizards are also clearly on their way out. The closest thing to a mechnical inventor is Saruman -- Tolkien clearly has a less "mechanical" vision of how humans should progress! -- but the return of the King is leading to a world of less magic and more humans. I can imagine someone inventing a cannon in the future. Anybody care to write fan fiction about cannon vs. balrog?
Jordan's magic is divided up into five elemental-like substances (the four usual suspects + spirit) consisting of the One Power. The male/saidar and female/saidin components of this are separate classes as well. Then, in a move that I'm still not sure is exactly parsimonious, he introduces a different power, the True Power, in the later books that is part of the "Dark One's Essence". Does that mean Shai'tan is being tangled around when one of the Forsaken weaves the True Power? Whatever is going on there, it's a bit like chemistry in that magic-users combine elements and, well, make reactions go, like fireballs or Healing. It's a nice system that conveys complexity and the need for skill in determining the power of different magic-users. You even have specializations in that Nynaeve can Heal well and Androl can make gateways but do little else.
The gateway magic itself seems to be something that Jordan only graadually realized could be so powerful, but it certainly became perhaps the hallmark spell of the series. Not only gates to transport or see new things, but spinning Deathgates were invented. Some of the rules seem arbitrary (thank goodness Trollocs can't go through Waygates) but there's an empirical process of discovery and trial and error in which the reader, and presumably the author himself, figures out the implications of these magical gates as we go along. In this way the magic is like science, and is somewhat technological as well.
Tolkien's magic is never emphasized the way it is in the later examples of the genre he founded. We never find out what it really is, or what constitutes strength in a field, or what makes it go. What we do see is usually explainable by other means, such as Gandalf's delaying the trolls till the sun comes out, or the mano-a-mano confrontation of Gandalf and Denethor. It's important to remember that Denethor is in some senses an equal of the great wizard Gandalf, so magic and political power overlap at least somewhat. Also, the political power of King Elessar is combined with a healing hand, another way in which social power and medical power overlap. Tolkien is saying something about the healing of all of creation, in which body and soul are joined and a good king is also a good doctor.
As you get into the story, Tolkien's magic seems more real and Jordan's less so. The fact of the matter is that fireballs are cool the first time and after a few go-rounds seem just like fancy cannonballs. Think of the difference between the way magic feels at Dumai's Wells and in the Last Battle. Even balefire becomes normal with overuse. The more powerful a detailed magic element is, like balefire, the less easy it is to work out its implications. What makes something disappear vs. lose a bit when balefire hits it? Shouldn't there be a popping sound when air is balefired out of the Pattern? (Note that Perrin finds out that creating a vacuum prevents the propagation of sound at one point in the last book!) Strength in Tolkien's magic is closely related to the human will itself, something that I think in our 21st-century enlightment we discount or even forget.
Perhaps Jordan's magic is ultimately mechanical and Tolkien's is organic, growing from life itself and the ties that bind creature to environment. Tolkien never forgot that "spell" means "word" at its root, and the very act of speaking and persuasion is therefore a form of magic, useful for healing or destruction. That makes Tolkien's magic more enduring, more relevant, and more real. The persuasive powers of Saruman's voice constitute a magic spell ultimately more chilling than balefire.
Next up in Part 3: People and Heroes