Thanks for the thoughtful replies! I hope to get back to the main topic of differences between the races in both authors' works again soon. For now, to avoid starting a new thread, I'd like to add two brief comparisons which do not concern that topic.
The name Bagshot shows up in both works. In Hobbit/LotR, it's Bagshot Row, Bilbo's home address. In HP, it's the surname of the witch who wrote the school textbook on the history of magic. In real life, it's the name of a village in Surrey, as well as of Bagshot Park on Bagshot Heath, a royal residence. (Thanks, Google and Wikipedia, for the quick infos! Interestingly, the list of occurrences of the name includes the HP character but not Tolkien's road name.)
Another similar element: as
this post points out, the One Ring is what Rowling calls a 'Horcrux' in her books. In both cases, it is used by the major baddie to split up his soul/power and must be destroyed to destroy him finally. I was not able to find a real life reference to this term and am not aware of its linguistic background. Perhaps someone has information on that.