Well… the two series are fairly dissimilar.
The Covenant series is a modern work, heir to all the arguments about borrowing and influence of previous works.
Tolkien’s series is seminal, to some extent, influenced by earlier myth cycles, certainly, but has been called the first real modern work of fantasy (although it shows a lot of pre-Hemingway influence in its style and prose – Tolkien was British, after all, and pretty conservative).
A difference I percieve in the two series is this: Tolkien’s characters are not only characters… but symbols.
Aragorn represents true nobility, in all ways and means; the Perfect Hero who never wavers… but even he should not carry the Ring, because of its corrupting power.
Boromir is a classic case of the Flawed Hero, the guy who thought he was up to the job (and so did everyone else), and it turns out he had a fatal flaw. Ghod, every Lit teacher I ever had beat this one to death.
Hobbits in general represent pastoral innocence, and the moral core and basic decency that’s supposed to result from this sort of upbringing. In some ways, Sam is the archtypical hobbit: not too swift, but certainly a strong, moral chap, not presumptuous or presupposing… but ultimately, the backbone of the entire quest to destroy the Ring. His only weakness is in his loyalty to his friends.
See what I mean? It could be said that investing symbolic value in the characters makes 'em “two-dimensional,” but I am inclined to disagree. I believe this is what Tolkien was trying to DO the whole time – create an epic in the old epic style, with characters who represent essential PARTS of that old style. The Covenant series, on the other hand, does not do this, at least not as obviously. The characters are much more modern (at least in part because some of them come from our world), and, more importantly, their styling is more modern … even the denizens of The Land.
Tolkien was working within a framework provided by Them What Came Before. Donaldson, on the other hand, was not.
The bottom line: Tolkien was looking backwards, trying to create an old-style epic for the modern day. Covenant, on the other hand, was trying to create a new fantasy novel, using concepts from the whole fantasy genre, but without the same old tired rehashes of Tolkien, Howard, and so forth. Hell, Donaldson has gone so far as to SAY that one of the reasons he wrote the Covenant series is because he was sick to death of Tolkien pastiches…