I know this is late, but...
I have read both LOTR and HP, and done extensive research on them...
the authors: Tolkien is a Catholic scholar, Rowling is a semi-pagan modernist...
WHO DOES THE MAGIC: Gandalf is a Maia, the equivalent of an angel, while the elves are the equivalent of ourselves before the Fall, In Harry Potter, Ron, Hermione, Neville, Luna, Harry, Draco, they are all normal children with the exception of "magical talent."
the detail of the magic, "mellon," the elvish word for friend is a much lighter spell then "Avada Kedevra," the killing curse, or "Crucio," the torture curse...
Also, as a side-detail, Harry Potter starts rather innocently with simple broomstick flying and the like, but by Deathly Hallows, they are discussing Horcruxes, which are the 7 things Voldemort separated his soul into, the DARKEST TYPE OF WITCHCRAFT IN HARRY POTTER... Rowling is a good writer. The content is what we should be concerned about.
If this doesn't convince you (as I don't have the time to write a fuller description currently) read the following letter, written by an ex-witch in 2000: https://www.pacinst.com/witch.htm .