For me, it's just the
Fellowship I like better as a movie. I think
The Two Towers and
The Return of the King are better as novels.
Regarding omissions I think it is due to the reduced attention span of a film audience compared to a reader, along with the fact that only three movies were planned, which themselves were quite huge enterprises, financially and logistically. There was a lot of ground to cover in the first one including the background and mythology, which I think was excellently done in the very first part of the movie where Blanchett/Galadriel told the essential background. That intro is actually among my absolute favorite parts in all of the three movies.
Regarding additions my guess is they were made due to an increased need for speed and thus, a good
flow, in the story building and perhaps the character arcs. Regarding the Arwen additions* maybe they did that to give the character of Aragorn some extra motivation in his participation, by establishing his romantic interest and close connection to the elves. Just a guess off the top of my hat

.
Regarding the omission of Tom Bombadill, another guess of mine is that covering Bombadill could complicate the story with a character that, if I remember correctly, only appears in the first novel and has no impact after that. Including Bombadill might also have lessened the perceived threat of the one ring for an audience, as Bombadill is the only one in the story which the ring has no effect upon whatsoever.
* Edit:
On a second thought they might have added Arwen to have one more female with some story in the movie. Otherwise there would have been only one such female, Galadriel, in a story which is full of male characters, including all the males in the fellowship itself.