Byrne called his changes "scraping away the barnacles" and insisted that it kept true to the spirit of the character. I don't think it did at all. Byrne's Superman came from a cold Krypton that he wanted nothing to do with. He was far less powerful and Byrne went out of his way to explain how every power worked, it no longer being enough that they simply did. (He decided Superman's powers were all telekinetic in nature. When I was a kid the only answer I needed to "How can he lift a whole battleship without it falling apart?" was "Because he's Superman!") Byrne's Clark Kent was a star athlete and his Lex Luthor was a rich business man who lived down the street from the Daily Planet.
Some people like those and the others changes he made. Fair enough, he's still mostly recognizable as Superman. But the changes he didn't get to make, well, those take it to a whole new extreme. Compiled here are a series of quotes from interviews, Byrne's official FAQ, and various posts he's made to his message board detailing the changes he was not allowed to make.
The Man of Steel that didn't happen.
On the subject of Lana and Lois:
"If I had really had the free hand some fans are convinced I did, I would have dumped Lois altogether and brought Lana back as Superman/Clark's one true love. But there were somethings that had to remain inviolable, and one was the Superman/Lois/Clark relationship."
Although he would later say,
"There was never any plan to, or even consideration of, dropping Lois for Lana. That part played out exactly as I wanted it to."
When asked about his more radical ideas,
"Lois was married in college, just for a couple of years. Wanted to play with how Superman would react to/deal with this."
Lois was actually dating Luthor when Superman turned up (but not his mistress, as Wolfman wanted)."
On the subject of Superman's power levels:
"DC would not let me pare Superman all the way down to original Seigel (sic) and Shuster levels (the flying was too much a part of the character, for instance), but I was able to scale him back so that, as I said at the time, he would have to "grunt and sweat" in order to perform at least some of his super-feats."
The low-powered strong man that Byrne seems to have wanted wasn't around for very long. Siegel and Shuster's Superman developed most of the powers Superman is famous for while they were still working on the character.
On making the reboot in continuity with what had come before:
"Simply put -- and at the risk of creating a whole treasure trove of ideas others can steal -- my basic idea was to do a story in which Superman screws up royally -- so badly that the earth itself (and everyone on it) is destroyed. He then spends six months finding a Higher Power who says Sure, I can make it all better for you. But there's a price!
––Anything! says Superman.
––The next panel the rocket lands in that Kansas cornfield."
On Kryptonite and Superman's journey to Earth:
"My original plan was to have the pregnant Lara come to Earth instead of the baby. I explained that I needed that because if Superman was once again going to be the sole survivor of Krypton, the only way we could demonstrate how lethal kryptonite is would be to kill Superman. So I came up with the idea of having Lara come to Earth so we could have a Kryptonian who could find kryptonite and die, so we would know it was lethal. But they thought that might be messing with the legend a little bit too much."
On the setting:
"No Metropolis. The series would be set in New York."
Byrne's ideal Superman, gathered from what we see here and what saw print, was hardly Superman at all. He is a man responsible for global genocide who goes to find some deus ex machina to undo his mistake for him. He comes from a world that is cold and unloving; his parents are strangers. His birth mother travels with him to Earth, only to die in front of the infant and the Kents. He's got some super powers, but he can't fly or see through things, he's not invulnerable and he's only strong enough to lift a car or thereabouts. He lives in New York, romantically pursuing and being pursued by his childhood sweetheart.
There's no Metropolis, Lois Lane (or if there is, she's divorced and dating Lex Luthor); there's no Fortress of Solitude or Supergirl.
You know, it kind of makes sense, because many of those elements seem less like the 'higher power' giving Superman a second chance than they seem like punishing him.
When summed up, I really have to wonder if Byrne had ever even read a Superman comic before coming up with that stuff.
"It could have been worse" will continue with the fifth Superman film that didn't happen. Soonish.