1. Originally the first film and the second were shot together and were more of a piece. However, the movies were split up into two films and portions of the story from what became Superman II were used in Superman: The Movie.
2. Director Richard Donner was fired from Superman II and director Richard Lester was brought onboard. Lester reshot large parts of the movie to ensure his credit for the movie. He had a different approach from Donner, and insisted on a wackier tone.
3. Gene Hackman basically didn't return for Superman II's reshoots, and Marlon Brando's portions were cut from the film.
While you likely didn't notice it much as a kid, and were able to give over a lot to superhero logic, Superman II may have the exciting supervillain fight, but it's tonally all over the place and the plot sometimes feels held together by bubble gum and tape.
It's difficult to know exactly what Richard Donner originally intended and what he would have left in back in 1980 or so, as some scenes are deeply cut from the theatrical release, especially trimmed for hammy comedy which can sometimes feel a bit burdensome in the version that's more familiar. But this version feels superior from a storytelling standpoint in so many ways that its hard not to want to see it as the "real" version, much as I consider the extended cut of Superman: The Movie as the official version and don't really bother with the original cut anymore.
Firstly, you can tell everyone is still feeling all right in this movie, that the reshoots and time on the set hasn't taken its toll. Reeve is buff, his hair in place and I don't think we get the pit stains. Margot Kidder, especially, still seems on, is always well lit, her hair seemingly professionally done, etc... And the cinematography seems better by leaps and bounds.
While the "big city gal fads" of the theatrical release provide some color, watching Lois squeeze orange juice is kind of a half-gag, and it's not missed in this version.
Also, the reveal of Clark Kent to Lois that he is Superman works terrifically better from a storytelling perspective than expecting that Superman would trip over a rug. Despite the fact the footage used is from audition film, it feels terrifically stronger from a story telling standpoint. I suspect that the scene would have only improved if Donner had managed to get it in front of the actual cameras.
What really seals the deal is the continuation of the father/ son story between Jor-El and Superman, and what each continues to receive from the other as, even in death, Jor-El gives the last of what he is over to his son. The cheesy appearance of Lara in the theatrical cut and the awkward transition from Superman to the white collared-shirted Clark doesn't occur and continuity feels much more intact.
And the Phantom Zone villains feel genuinely more menacing under Donner's direction and oversight.
In short, if you've never seen this cut, I highly recommend revisiting the movie through this version.