A high degree of HtH skill--either powered or powerless--is not really part of Superman's core narrative yet. You see writers do what they will with this aspect of him a lot.
Cyclops being quite skilled HtH (but not a true MA), as well as an experienced and cagey combatant, is pretty core to his mythos, IMO.
So on the whole, I think Cyclops takes this, but Superman surprises Scott by being very, very hard to put down. Supes has a Rocky chin and determination.
However, some of the more skilled Superman portrayals could really make this a contest or even be favored.
Never let anyone else define you. Don't be a jerk just to be a jerk, but if you are expressing your true inner feelings and beliefs, or at least trying to express that inner child, and everyone gets pissed off about it, never NEVER apologize for it. Let them think what they want, let them define you in their narrow little minds while they suppress every last piece of them just to keep a friend that never liked them for themselves in the first place.
It IS part of Cyclops's bio that he's proficient in two martial arts, and a trainer of other X-Men in said martial arts. How about you focus on the actual topic at hand instead of trying to get a rise out of people.
Superman beats expert practitioners of every martial art known to man. He's beaten Luthor, Who has been trained in combat by Amazon's. He himself has been trained by The two greatest HtH combatants in the hero community and street levellers and top tiers, respectively. He consistently fights living embodiment of combat on cosmic and mythical scales as a peer.
Pillow Biter has known these facts for the near 2 decades now that I've known him online, yet he consistently chooses to downplay the facts.
Now I can see Cyke's tactical mind being his main advantage.. and even then..
Luthor was considered to be a substandard student by the Amazons, and with Diana, her skills are an equaliser that allow her to compete with his superior strength and durability.
I'll argue with anyone that says that Superman doesn't have legit fighting skill, but you can't let the pendulum swing too far the other way either.
People saying either man wins easily are talking out their ass, tbh.
Powerless Superman fell off a building into a dumpster and tore it apart.
Powerless Superman took hits from Earth-Man (stacked stats of Timber Wolf, Blok, and arguably Ultra Boy's strength and Night Girl's stats) and then re-entry heat.
Powerless Superman seems to win the feat war as well as this fight.
__________________ Bluewaterrider: "I'm surprised that a Skyfather like Zeus defeated Hulk when Zeus' Top-Tier son Hercules has lost to Hulk."