My review of Superman II covers the behind-the-scenes shenanigans that went into make the followup to the original Superman, so I'll try not to repeat myself too much. Superman II:The Richard Donner Cut (2006) is an attempt to restore director Richard Donner's original version of Superman II. Donner, who directed the original Superman, was supposed to finish the sequel before he was unceremoniously fired and replaced with Richard Lester over creative differences with the film's producers.
This version of the film restores much of the footage Donner shot, dumps substantial portions that Lester filmed, and places different emphasis on different points. It's not a perfect director's cut. Gaps that Donner wasn't able to film back then are filled in with Lester's material. While it fixes some flaws with Lester's version, it creates a few new ones, most notably at the end, but regardless of which version of Superman II you watch, it's hard to be disappointed.
Donner's Cut follows the same plot as Lester's. General Zod and his two underlings, Ursa and Non, escape from the Phantom Zone (where they were imprisoned by Superman's father Jor-El) and fly to Earth, where they discover they have immeasurable power and decide to conquer the planet. Meanwhile, Lois Lane has figured out Superman and Clark Kent are the same person, and Superman, over the objections of Jor-El, decides to give up his powers to be with her.
Of course, Donner adds previously unseen footage, most notably Marlon Brando as Jor-El, whose character was written out and replaced with Superman's mother after legal and financial disputes between Brando and the producers. This helps strengthen the sequel's ties to the themes and plot of the previous movie and fixes at least one notable plot hole (by explaining how Superman gets his power back). Other additions are minor: when the Kryptonians attack the White House, Zod steals a soldier's gun and kills some people with it, just for the heck of it.
As I said, there are problems, whether as a result of being what Donner intended all along or because the restored version was limited to what footage was available. The decimation of the small town by the Zod's group feels truncated and choppy, and the film ends with Superman once again resorting to flying to around the world so fast he undoes time. Unlike in the first Superman, he doesn't just undo the climax; he undoes the whole movie. Sure, he's learned his lesson about his responsibilities, but it returns everything else to where it was when the movie started. Plus, it's a recycling of the original movie's ending (reportedly, this was originally only supposed to be the end of the second movie, but it raises the question as to how the first was supposed to conclude).
If nothing, Superman II is an interesting experiment: how do two filmmakers interpret the same material? Lester went for comedy and comic book action. Donner went for epic modern myth. Both work in their own ways, and both have their own flaws. Either way, it's a worthy sequel.