Believe it or not, this is something I've given some significant thought to...and, brazen as it may be, I think both the Post-and Pre-Crisis reasoning are actually...not wrong, but lacking in correctness, a bit. I just never bought that he gets "all" his powers from the yellow sun, full stop.
Most comics touch on the 2 big reasons for Superman's abilities, which everyone knows about:
1] The Gravity
2] Earth's Yellow sun.
I postulate that there is a third reason, which essentially goes back to his vastly different Kryptonian physiognomy, not just his cell structure.
In a 2000 reprint Millennium edition of Superman #1, 1939 , it reads that Clark's main powers, as evidenced on one 8-panel page are that he could...
Hurdle sky scrapers, Leap an 8th of a mile, run faster than a streamline train and nothing less than a bursting shell could penetrate his skin!
Later pages in this same book, a page offers _"Scientific Explanation for Superman's Amazing Strength--!" saying that:
Superman came to earth from KRYPTON, whose inhabitants had evolved, after millions of years, to physical perfection....The smaller size of our planet, with its slighter gravity pull, assists Superman's tremendous muscles in the performance of miraculous feats of strength!...Even upon our world Today exist creatures possessing SUPER STRENGTH! The lowly ant can support weights hundreds of times its own. The grasshopper leaps what to a man would be the space of several city blocks!"
"It is not too far-fetched to predict that someday, our very own planet may be peopled entirely by SUPERMEN!"
A story in said-same reprint goes on to elaborate at other points of his different structure and indestructibility. An accident occurs in a mine shaft, where "poison gas" is released. Superman enters into the shaft freely, "his physical structure unaffected by the gas"...
This hints that his muscles, nerves and cells on a whole are so far advanced they are highly resistant, if not invulnerable to toxic fumes as well as terrific physical force. A written portion in this same book, penned by Jerry Siegel, recounts: "....
...with amazing rapidity, he stripped off his glasses and outer garments, revealing himself clad in a close fitting costume and flaring cape. In this apparel, it was apparent that he really possessed a fine physique of breathtaking symmetry. One lithe leap brought him to the window sill. There, he poised momentarily while his keen telescopic vision surveyed the vicinity
So apparently, the Pre-Crisis account of near physical "perfection" accounted for super strong senses, as well [at least telescopic, if not microscopic & x-ray vision]. This goes to what I consider the 3rd, base source of at least a portion Superman's powers
3] Highly advanced Kyrptonian physiology, that is, in some ways, deeply different from humans.
Oh, it maybe humanoid, yes, but not completely human in any fundamental way, other than its exterior design. Now granted, everything I'm putting forth here is somewhat speculative; there have been only occasional references to any of these elements in the canon comics. As such, most of this is put forth via observation. As such, the differences in a Kryptonian body which we may deduce contribute to this physiology are as follows.
1. A more evolved form of muscle cells and tissues, combining both slow-twitch AND fast-twitch properties. These "pink muscles" would allow Superman to produce a greater amount of force, without tiring , and for far longer periods. They would also probably have a naturally higher number of mitochondria [the cellular powerhouses] which would produce greater contraction ratings in each fiber. In other words, if there was no yellow sun and equal gravity, and Superman was placed against an earthling of equal size, height, weight and mass, his muscles would still work, on average, 10-20 times better and longer, making him an average of possibly 20 times stronger.
2. A cell structure that more efficiently copies itself, allowing the cells to flush toxins, renew themselves and make perfect clone cells without [or at least with a highly retarded rate of] degradation. This would mean every cell in his body, even without a yellow sun, produces less waste chemicals from break down, and more quickly reproduces/regenerates itself from damage. This would essentially give Superman a "healing factor" or sorts, as he would not easily sustain major tissue damage. He would also, consequently, age more slowly.
3. A corded muscle structure. Most human muscle is smooth and flat; it's possible Kryptonians have muscles which are linked like braided ropes or chains, meaning the fibers are entwined in a latices pattern. This phenomenon is real, and can be seen in other bipeds, like simians, who, pound for pound, are stronger than humans of equal weight. This would naturally make them stronger and more durable, physically.
4. Adaptive antibodies in his immune system. Superman's immune system would need to be more evolved to be able to "resists poisons" as he does, or at least allow his structure to adapt to said poisons better than ours do. It's likely that the harsher Kryptonian environment produced "super bugs" which his immune system developed normal defenses for, so anything from this planet wouldn;t even register as a threat to it.
5. A more advanced chromosomal structure. Consdiering there is only a 10% difference between the DNA of a virus, and that of a human, yet we are radically different in some ways, it's not illogical to think Kryptonian physiology is different on a chromosomal level. So even in terms of chromosomal development or possible number, on the fundamental level where new genes are created, Superman's body has a natural edge after thousands more years of evolution. These chromosomes would also account for the organelles in his cell structure which absorb, condense and store solar radiation, allowing for the photo-voltaic affect which allows him to produce even MORE physical power.
Bonus: Chromosomal differences would also easily explain why Superman simply can't have a child with an earth woman; we're vastly different, even at the genetic level.
6. A more advanced neuro-synaptic structure, which accounts for Superman's greater memory, senses, and faster nervous system, while also attributing in part to his strength and speed. Logically, his nerves would need to fire faster to power more evolved muscle tissue at a greater rate. This likely also means that Superman largely perceives everything around him in "slower motion" than most humans, and, without the sun, he would likely still be capable of moving & thinking between 40 - 90 times faster than an average person
8. Greater abundance of stem or progenitor cells, which would also mean greater capacity for developed sensory cells. Where as a human has 2 million odor sensitive cells in his nose, Superman might have 20-10,000 times more, for instance; same thing for his sense of sight, taste, touch....even some senses we might not know about. This would explain his vision, even for him being able to see in the entire spectrum; many earth animals already see outside visible light spectrum, yet their eyes aren't "super" evolved.
9. Actual development of new regions in the brain, or greater access to all regions. The prefrontal cortex is really the central structure in the human brain which accounts for our higher development compared to most other species. Taking it a step further in Kryptonian bodies, their brains may have developed regions which can allow for psionic abilities, such as telepathy, eidetic memory, and limited telekinesis. This telekinesis would need to be amplified by energy from the yellow sun (else only done via extreme concentration). This would be one way to account for Superman's ability to fly under a yellow sun; the only other option is some form of graviton manipulation via some new organ.
10. Personal gravitational control organ. Lex Luthor theorized this in Superman: Birthright, and it makes sense. It's basically some type of internal structure or structures, like lymph nodes, which control a personal gravity field would allow him to [a] fly at will with enough energy to control it, [b] maintain his molecular density on this or any other lighter planet [c] explain why his body "instinctively" stays "planted" on earth, as opposed to Superman moving on earth the way a human moves on the moon, and why his muscle doesn't waste away while being on this planet.
All of these would be latent, normal abilities ANY Kryptonian would have on their planet, just on comparatively LOWER levels; this would, largely, be the result of that planet's gravity, environment, atmosphere and cosmology....as well as perhaps a comparatively quicker rate of their race's evolution weeding out many of their weaknesses.
So, on a super-giant world like Kyrpton, which could easily be 50 times earth's size or more, and theoretically made of even heavier materials.... these abilities are fairly common. While "super", yes, they are by no means God-like due to the planet itself "limiting" their ability, and the lack of a super-empowering Yellow sun. If on the other hand, they had a yellow sun on Krypton, their physiology would be super energized, but perhaps still affected by the gravity & environment of the world, making them....mmmm, perhaps 1/3 - 1/10 as strong as Superman in an Earth environment is.
On Earth proper, however, under "0.03 standard Kryptonian Gravity" [Superman: Birthright #1 2002], and with the cellular enhancing power of the yellow sun multiplying this increase by a factor of anywhere from 100 to 1,000,000,000 its not inconceivable that his latent abilities would ALSO be enhanced to such levels, making him be able to move continents with ease, think at speeds faster than light, and counteract our gravity completely by telekinetically "propelling" himself through space.
Again, though, this is mostly conjecture.