Unsurprisingly, there's really no situation where Cyclops comes out on top, as is the case with most things related to Superman. His heat vision is off the charts and powered by the sun. It's no wonder then that Cyclops would lose this one.
Superman is considerably more physically powerful than Cyclops and presumably Superman can sustain projecting his heat vision far longer than Cyclops projecting his optic blast.
Are Darkseid's Omega Beams stronger than Superman's heat vision? Heat Vision and Omega Beams have met more than once. Superman has a direct fight with Darkseid and they both use their respective eye blasts. and in this case Omega Beams won.
As his powers developed and became more defined, however, Heat Vision became distinguished as an individual power. The temperature of heat vision or a laser beam is stated to be 5000 degrees (presumably Celsius), making it capable of burning through the toughest steel, material and armor.
If (and when) he needs to protect himself and others in extremely hot environments, heat vision will be no use to him. It might even be the colder option in this particular scenario.
Darkseid once boasted that no living being had ever withstood the full force of the Omega Effect, but Doomsday and Superman have both withstood the Effect. The Cyborg Superman has demonstrated a degree of resiliency to them as well.
Cyclops emits beams of energy from his eyes, described as "optic blasts", which have the appearance of red light and deliver massive concussive force. The beams cause no recoil or heat, but are tremendously powerful, and can be used to rupture steel plates and pulverize rock.
As soon as they regroup, Wonder Woman has the support to try and blind Darkseid. He shoots an Omega Beam right at her, but she blocks it with her gauntlets. This throws him off just enough to give her the advantage.
Even breaking the rules of this comparison and factoring in a world where Homelander can attain access to a supply of the rare mineral Kryptonite, Superman's superior tactical knowledge and combat training would still likely best Homelander in a Homelander vs Superman fight.
That being said, while Superman doesn't seem to discharge too much in the way of concussive force with his Heat Vision, as many other Energy attacks do, Heat Vision is still likely at least a small Planet-busting attack, for the very simple reasons of its range, heat and energy output, even though this still does ...
If Mjolnir was doing nothing then yes. Superman will eventually melt Thor's hammer. But if it responded to Superman trying to destroy it then it would definitely won't go down so easily. Superman's heat vision is capable of melting things things and people.
Similarly, Cyclops, one of Xavier's original five X-Men members, was able to defeat the Juggernaut not using his mutant abilities, but his extensive strategic knowledge.
Can Superman fry Thor's brain with his heat vision? Most likely not, atleast not in a quick fashion. Superman's heat vision is ridiculously strong, but Thor has withstood greater forces in his lifetime.
I'm going to max power!" before using a concussive blast so powerful it begins to strip the skin from Hulk's body. It isn't quite enough to stop him, but that impact puts Cyclops in a small group of people able to damage Hulk in his strongest form.
Power regulation disability: Due to a psychological trauma and physical injury at a young age, Cyclops is unable to control his optic blasts. In connection, his eyes have become more reliant on the ruby quartz he uses rather than affecting change to the injury.
The lenses of his glasses are the same ruby quartz as his visor. The lenses filter out the particular wavelength of his optic blasts so they just kind of stop right there.
He's a ruler, he like to prove he's the threat, not just his omega beams. Just think in real life terms, if someone had a gun, you would most likely only find them threatening because of the gun, as soon as the gun is out of sight you no longer see them as a threat and may even plan an attack. Who's more threatening.
Phobia: Incredible as it may seem, Darkseid fears his father, Yuga Khan, more than anything else; Yuga Khan is the one being in the universe far more powerful and evil and was worse of a tyrant than even Darkseid.
Is Godzilla's atomic breath hotter than Superman's Heat Vision?
After all, the temperature of the MonsterVerse incarnation of Godzilla's atomic breath is approximately 36,032 Fahrenheit at its weakest while the lower end of Superman's heat vision has been confirmed at around 5,000 degrees (at least during the New 52).
Unsurprisingly, there's really no situation where Cyclops comes out on top, as is the case with most things related to Superman. His heat vision is off the charts and powered by the sun. It's no wonder then that Cyclops would lose this one.
