Easterhay said:

Well, Jackson has wrought more changes on his Tolkien films in a lot less time than it took Lucas to start revising his films so there's another difference. So god only knows how many versions will exist of both LOTR and The Hobbit in, say, thirty years' time.

Jackson has wrought exactly one change on the home video releases of the theatrical edition of LOTR. He removed a car that drove through the Shire when the Hobbits were reflecting on what it meant to leave (IIRC). I am personally rather offended by this--I had written a 26-chapter fanfic loosely based on Tolkien's time-travel story in The Lost Road, which required me to construct a hypothetical intermediate language between Adunaic and Old English, all to explain the presence of a car in the Third Age. When I saw that Jackson had removed it, I deleted the whole thing in a fit of rage. But I cannot argue removing the car significantly alters the film, or that a reasonable person would want it put back. It was not an intentional element of the film, not the work of one of the many artists and artisans who contributed to the work.

(If I wanted to be annoyingly pedantic, I could point out that there were two theatrical editions of the first one or two films--the initial release, and the re-release with the teaser for the next movie. You cannot watch the re-release with an integral teaser, but the teasers are available with one or both home video versions.)