For starters, Willard's character is much more human and his extended mind torture at the hands of Kurtz (Marlon Brando) is way more unsettling than the theatrical or redux cuts. His real life depression at the time is evident onscreen many-a-time.
Kilgore (Robert DuVall) makes an additional appearance later in the film, following the boat by chopper and yelling through the speakers "I want my surfboard back, Willard!"
Johnson's (Sam Bottoms) gradual insanity is expanded too: He opens fire on animals (water buffalo) for no reason other than "I control the destiny of all that enters my space". Later he joins Kurtz's followers and assists in the torturing of Capt. Willard...
We learn that the Photojournalist (Dennis Hopper) is totally bonkers and that the reason why we don't know his real name is because he has been brainwashed by Kurtz and has totally forgotten it in his madness. We also see his demise, at the hands of MIA trooper, Colby.
Colby (Scott Glenn) has certainly had the most cutting room floor treatment, as his character is fleshed out to the max in the workprint. He watches over Willard, talks to him and develops a cold (but trusting) relationship. When it's his time to pop off, he begs Willard on his dying breath to say goodbye to his wife and to kill Colonel Kurtz "at all costs."
As for Kurtz, during the caribou sacrifice, Willard terminates his command to The Doors' 'When The Music's Over' (again in it's entirety) with a single machete chop as Jim Morrison yells the last line "Until the eeennnddd!!!"
And that's when the film does end, cutting to black. No leaving the compound, no "the horror", just on that one fatal blow with no credits.