"So really, I see this as inconclusive. The main difference between King Hyperion and regular Hyperion, is that KH is definitely stronger and has a much better showings and track record than regular Hyperion. However, his only major advantage is a small AP advantage that doesn't mean that much. Superman has a few more tricks up his sleeve but I don't feel that any of them are enough to definitely give him the edge. There's a good level of canceling out here."
I still say Inconclusive and stand by the reasoning that LordUrien935 quoted.
I'll also say this, the two do have a distinct quality that seperates them: Supes has better stamina while King has his Atomic Vision.
Superman can potentially outlast King but that doesn't stop King from being able to beat him down nor is King going to drop from exhaustion anytime soon. As for King, his Atomic Vision is really, really potent. I mean, it literally got through King's durability and left him crippled with a single blast. In addition, he killed Namora, who was a match for Namor, underwater with a single blast of it. However, Superman is resistant to energy attacks ontop of his natural durability so...yeah, they're just a tad too even in most regards.