Tolkien geek here...

Rating: Null/10 (22 December 2002)

And I have to say I thoroughly enjoyed this movie. I agree with others that, at times, the scenes changes were too rapid, but perhaps that can be corrected in the extended version. (Fellowship's extended actually made that movie flow better.)
As for differences between the two movies: It is a sequel (by the definition of the word), but unlike other sequels it has a different feel than the first movie. This is the same as the books.
FOTR was more personal and suspensful (which Jackson translated well on the screen) while TT is more epic.
Now, I noted all the changes in the story in both movies, and generally the reasoning for such changes is as follows:
1) The necessity to cut down on named characters. Jackson et al could only choose from so many of Tolkien's characters. And remember there were quite a lot of them. Examples: Arwen replacing Glorfindel and Eomer replacing Erkenbrand. Both examples show Jackson replacing a character that only occurs once in the book and giving that spot to another character. Erkenbrand, even in the book, is far more important than his character. The reader knows who he is through dialogue and only sees him once. Why not banish Eomer instead of imprisoning him and let HIM be the force that comes to the aid of Helm's deep, not some character that won't ever be mentioned again.
The only problem, is that Eomer and Aragorn bond in the book through the fighting at Helm's Deep. Jackson, instead, gave much of those lines to Theoden, giving his character more importance and more strength.

2) To draw in those viewers who've never been able to read the books. Most people who haven't read the books attempted to and were not able to get through them because of the archaic, and generally poorly written (not poorly conceived or plotted, both of which Tolkien did an outstanding job on! And remember I AM a Tolkien geek!) narrative. If TT had been done exactly as written, all the action would have taken place in the first half of the movie and the latter half would have been, mostly dialogue. I don't think even a diehard Tolkien fan could have sat through that.
The movie does away with that because you don't describe the people/places/things with words. You use images. And you can make the movie sets/costumes/items as visually detailed as the books were verbally detailed without overwhelming the viewer. This also explains the Rivendell scene with Elrond and Arwen. It drives home the point that is hinted at in the books but is not spoken. The Elves don't really want to get involved. In fact, when Elrond finally commits he send a small contingent, which in the books only has a few elves. The others are actually Men. As for his trying to separate Arwen and Aragorn, it makes sense for an elven father to think that way, especially one that descended from such pairings. And it also explains to the new viewer why it's bad for Arwen.
3) Time constraint. This one is pretty easy to understand. There's a lot of stuff in the books and to get it all on the screen (but not, necessarily, do it justice)would take a movie that is a lot longer than three hours. And if you produced a movie that is just like the book, who would watch it? Tolkien fans only. Those that could not sit through the books would not sit through that movie either.
4) One of the most important reasons for any changes is to add more urgency to the movie and to drive home the point about the ring. For example, in FOTR the book there is something like 40 years between Bilbo's party and Frodo's escape from the Shire. And when he actually does leave, he doesn't run and leave everything behind, he puts his house up for sale, buys a house in Buckland and SLOWLY arrives in Buckland to action finally start. If that had been done in the movie, people would have walked out. The moive adds urgency but shortening the time and having Frodo make a sudden and panicked escape. In TT the movie, Faramir is drawn in by the ring just like Borimir and others, to drive home the point of its power. This reason explains many choices made in the movies: why the ring was packed away and not kept on Frodo's person; why Frodo stands before the Nazgul in Osgiliath; why Faramir is a different character in the movie than the book. (Also note, he doesn't go into his family trouble in the movie the way he did in the book. This was done because of time constraint, I am sure.)
Now, for those of you who are upset about missing chapters (especially Shelob) go get your copies of the books, and put your finger in RotK where the story actually ends. Now compare the size of the actual story in that book to the other books. Notice something? RotK is much shorter than the other two, once all the publishing padding of appendices is removed.
Go see the movie again and listen closely to Gollum. You will find your answer to where's Shelob in his words.
Now, I have to admit I was a trifle disappointed with some of the changes until I came home and flipped through TT to see the original way it was done and realized, that in order to make a GOOD movie, those things had to be changed.
One has to remember that, for the most part, movies and books are totally different things. A reader has time to read pages and pages and pages of background stuff. A movie viewer does not.
And even if this had been a mini-series for TV, there still would have been changes. Anything not necessary to the story would go. (Like Tom Bombadil.)
I saw this movie with people who'd never read the books (some of them who don't even really like or understand fantasy)and this is where Jackson's work paid off, they all loved it. They could, more or less, follow the plot. And, more importantly, they all want to go see it again.
In summary, Jackson's movies are very faithful to the spirit and plot of the books and basically treat the story in the only way a movie can.