The Wikipedia page referred to gives an exhaustive list of the differences, in terms of deleted scenes. There are indeed many scenes in the Final Cut which were omitted from earlier releases. But this is not really to the point.
The answer to the question is what differences those changes have made to the plot.
The Final Cut (2007) is a very different movie, in terms of plot. Harrison Ford is always hunting for replicants, but never before did the director's real vision emerge. Ford's character is defined by the differences in what he does in those changed scenes. The differences boil down to whether he falls in love with the replicant, Rachael, or not. And whether he, Deckard, is revealled to be a replicant himself.
I originally saw the international edition on its UK release in 1982, and most recently saw the latest version, the Final Cut director's version edited by Ridley Scott, and I was amazed by the difference. The Final Cut is a significantly better movie; and I finally understood the reasons why the director was so unhappy with the 1982 release, which the studio had forced him to release in that form, such that - according to press reports at the time - he had tried to disassociate himself from the movie.
The plot changes made in the Final Cut are all for the better, IMHO, giving real emotional depth to a picture which was, on its original release, little more than a routine Bruce Willis style shoot-em-up. Deckard and Rachael finally become real people, with real motivations and real emotions, in the Final Cut; which is deeply ironic, given that in it they are both depicted, by a very subtle implication in Deckard's case, as not actually being human.