Well, it's late (or early depending on your orientation) and I just got off of a long shift at work so I may not be coherent. However, I wanted to throw in my two cents' worth.
I've never read the ring cycle so I can't discuss that but I've read both LOTR and the Thomas Covenant series.
I see the coincidences with a ring being used as incidental. Covenant's ring is a symbol for him, his own personal talisman if you will and is only powerful because of the material it is made of (it's been a while since I read the entire series so if this is incorrect, someone please correct me). Sauron's ring is an object of power, created to be used as such. To me, that makes them completely different.
Other than the fact of the rings, I don't see any similarities at all. The Land is quite different with unique resonances that don't even remind me of Middle Earth. All of the races and their belief systems are unique as well. Throw in the fact that Covenant, unlike Frodo, wasn't originally a part of the land or its peoples and you have more differences.
Bah! They aren't the same stories, one didn't steal from the other and that's all I've got to say on the matter. I'm yawning too much to say more
.
G'night all...