Like Superman in Byrne's comics, Superman in the Fleischer cartoons was less powerful than the Pre-Crisis Silver Age/Bronze Age comics Superman and the popular Christopher Reeve Superman.
Like Clark Kent in Byrne's comics, Clark Kent in the Fleischer cartoons showed some confidence, some seriousness and self-reliant aggressiveness as an investigative reporter, and scooped Lois out of writing the story in "The Mummy Strikes." The Fleischer Clark Kent didn't act like a Jerry Lewis-esque bumbling buffoon goofball like the popular Christopher Reeve Clark and wasn't a TV news anchor like the Pre-Crisis Bronze Age comics Clark.
Primarily the Fleischer cartoons provided John Byrne with an influence for Superman battling gigantic monsters that give him a physical challenge. Like Superman in Byrne's comics, Superman in the Fleischer cartoons fought a lot of monstrous (often gigantic) super-powered foes that gave him a physical challenge that he had to struggle to defeat - the giant robots in "The Mechanical Monsters," the giant dinosaur creature in "The Arctic Giant," the giant gorilla in "Terror on the Midway" and the giant mummies in "The Mummy Strikes" and the race of hawk people in "The Underground World."
That all had an influence on John Byrne. The story where Superman battles the gigantic Host in Mummy bandages is even titled "The Mummy Strikes" (Superman #5 (1987)) obviously even titled after "The Mummy Strikes" Fleischer Superman cartoon from 1943.
Also in that issue Superman has a dream flashback about his battle against the giant Hounds of War robots from Apokolips with Wonder Woman which took place in the Legends mini-series.
Superman fought many gigantic foes in John Byrne's run. The giant creature created by the Serabite Stone (Action Comics #585 (1987) "... And Graves Give Up Their Dead...").
The giant Pacifier/Glommer of Apokolips (Superman #3 (1987) "Legends from the Darkside").
The giant towers (Action Comics #587 (1987) "Cityscape!"). The gigantic Rampage (Superman #7 (1987) "Rampage!"). The giant Klaash robot (Superman #10 (1987) "The Super Menace of Metropolis"). The giant strange microbes, giant tentacle organisms (Action Comics #589 (1987) "Green on Green"). The giant Chemo (Action Comics #590 (1987) "Better Living/Dying Through Chemistry"). The giant Highmaster (Superman #14 (1987) "Last Stand!").
The Prankster's giant rubber flower (Superman #16 (1987) "He Only Laughs When I Hurt!"). Professor Killgrave's giant Juggernaut (Superman #19 (1988) "The Power that Failed!"). The giant Dreadnaught (The Adventures of Superman #442 (1988) "Power Play").
Also Superman fighting giant foes dates back to creator Jerry Siegel's "Giants of Doom Valley" (1940) where Superman fought giant men and giant vultures, that was published in the Superman newspaper strip.
Also Superman fighting giant foes dates back to creator Jerry Siegel's "The Chosen" (1940) where Superman fought a giant spider, that was published in the Superman newspaper strip.
Also Superman fighting giant foes dates back to creator Jerry Siegel's "Bandit Robots of Metropolis" (1940) where Superman fought giant robots, that was published in the Superman newspaper strip.
Superman also fought the giant robots on the cover of Action Comics #36 (1941). Superman fighting giants also dates back to Superman #8 (1941) "The Giants of Professor Zee" by creator Jerry Siegel. Superman fighting giant creatures also dates back to Superman #12 (1941) "The Beasts of Luthor" by creator Jerry Siegel where Superman battled a giant octopus, a pair of giant lions and a giant reptile. There were also giant ants. So Superman versus giant monstrous foes is not just faithful to the Fleischer cartoons, it's actually also faithful to Jerry Siegel's vision.
John Byrne explained, "Part of the homework I did preparing to take on Superman was to study up on as much material as I could find. First the comics, of course, and there I sifted through almost fifty years of often very contradictory material. I looked at the serials, the George Reeves TV series, the Fleischer cartoons and, of course, the Christopher Reeve movies. I also checked out how the character had been handled in his Superboy adventures. With all that percolating in my brain, I took the parts that seemed to be most consistent thru-out, and then added a few modernizations."
John Byrne also commented, "George Reeves introduced me to the character, so he will always have a special place in my heart. As will Wayne Boring, who was principle artist when I started reading the comics. The Fleischer cartoons gave another kind of life to Superman, as did Christopher Reeve."