I'm just curious, how was Tolkien's version more "Christian", so to speak, than Jackson's? I ask because I'm a Christian and don't have a problem with the film version. I haven't read the books (except for The Hobbit) but my understanding was that the scene in the book was like the cartoon; Gollum takes the ring, dances around and just slips off the edge without any further struggle with Frodo.
Frodo still gives in to the power of the Ring in both versions, he battles Gollum over it in both versions, what's wrong with him struggling all the way till Gollum goes over the side? I know PJ actually filmed an alternate version of the scene where Frodo *pushes* Gollum off the edge, but that isn't what happened in the final movie.