That's really hard to say. As far as places are concerned I think the film has it down pat. The Shire, Bree and The Prancing Pony, Rivendell, Moria were all fantastic and more glorious and fantastical than I even imagined. And Lothlorien was absolutely awe inspiring.
As far as characters, that's a little tougher. I think Gandalf, Bilbo, Sam, Arwen (her increased roll aside) Gimli and Legolas, Aragorn, and Galdriel were all great. There are some issues with the other characters but I think all in all, they are fairly minor issues.
Where changes in the plot and story are concerned I think JRR Might have had some real beefs but, just liked fans, postAuthorIDs often expect the impossible in interperatations of their novels. There are many exceptions however. I've seen many film adaptions where the postAuthorID wrote the screenplay, or at least had a great deal of input in the making of the film, and there were changes made that were far more drastic than anything we've seen in FotR.
Anne Rice went on a crusade against Interveiw with the Vampire telling fans of the book to boycott the film and blah blah blah, primarily because of the choice of Tom Cruise as Lestat, but also for other reasons. She took out full page ads in major newspapers all over the country trashing the movie. Then she saw the film ...and absolutely adored it. Having read the book and seen the movie I can tell you, they were far from identical. Lestat even flies in the film which he most certainly could NOT do in Interveiw. His ability to fly came long after the events in the first book...
Anyway, the point is, some postAuthorIDs understand that they have to make changes to the novels when they adapt them for film. Many others are satisfied if the overall themes and feel of their works are left intact, which, in the case of FotR, I think they were.
As to which type Tolkien would have been, who can say?
If you want to see examples of true hatchet work, go read any Dean Koontz novel, and then go see its film adaption! Koontz described every movie version that's been made from his books as "the spawn of hell" and he's absolutely right. They bear little to zero resemblance to the originals. The Watchers is a good example. Excellent book, ridiculous movie.
WWGD: What Would Gandalf Do?