DISCLAIMER: I do not own Superman, the Justice League or Devil May Cry.

Superman flew towards the ground, having heard cries of panic. When he reached the ground, a small-built woman was backing away in terror from a white-haired man in a red coat, who carried a large sword. Superman landed between them, flexing his fists. "That's enough! Back away!"
The man in red smirked. "Good timing. I could use a good fight. This weakling doesn't cut it."

Superman charged forward with such speed as to create a sonic boom, and swung his fist at the man. To his amazement and disbelief, the man jumped aside, matching Superman's speed. The man smirked again. "Not bad. Just because you dress like a pansy doesn't mean you are one."
Superman fired his heat vision at the man, but the man's sword flew into his hands, blocking the laser beam. The entire sword heated up to a temperature resembling that of the sun's core, but the blade did not melt, and the man's grip did not weaken at all. "Nice. I'm curious to see how fast you could cook my pizzas for me. They always take forever to cook. And they always have olives on them no matter what I do."

Superman swung his fist into the man, launching him up into the air, watching as the atmosphere parted and the man in red was sent into orbit. Suddenly, there was a flash of red light in space, and the man in the red coat reappeared, falling smoothly back towards the earth, landing on his feet in front of Superman, red energy still arcing across his body. "Nice punch you got there." The man in red cracked the cramps out of his neck and back, impressed by the incredible force of Superman's punch.

Superman flew at the man in red, swinging his fists at him with enough force behind each punch to throw a skyscraper to the moon. The man in red, moving at a speed similar to Superman's own, dodged every attack, before finally bringing out his sword and swiping it at Superman. Superman held up his arm to block the sword, but the blade, to his horror, cut through his arm like it was warm butter. The blade would have cut Superman's arm off and probably cut him in half if the man in red had not halted the strike just as the blade penetrated Superman's flesh, stopping just short of the bone.

The man in red stepped back, lowering his blade. "I heard from Trish that you were completely vulnerable to magic, so I knew my sword would cut straight through you. Truth is, I don't want to kill you."
Superman lowered his injured arm before speaking. "Who are you?"
The man in red turned his back on Superman. "My name is Dante. I hunt demons."
Superman put his uninjured hand on Dante's shoulder, turning him around to face him. "If you aren't evil then why were you attacking that woman?"

Dante gestured over to the woman, who moved closer to them, her eyes glowing red. "I was hoping one of you would kill the other. I could have easily killed both of you, but I called for help because I wanted the superhero and the son of Sparda to weaken each other, and hopefully even kill each other, but I can finish this just as easily myself. I will devour your souls!"

Superman cracked his knuckles, angry that a demon had tricked him into defending it from what he now knew was a fellow hero. The demon charged forward, the form of the human female vanishing to reveal the form of a grotesque demon with long claws and razor teeth. Dante pulled his guns from his coat, red energy arcing across them, while Superman's eyes glowed a similar shade of red, his heat vision priming to attack. The demon was destroyed before it had taken two steps.

Cleaning up the ashes of the demon, Superman and Dante shook hands, Dante cringing slightly at the sheer power of Superman's grip. Dante made a mental note to focus a small amount of devil magic into his hand next time he and Superman shook hands so as to even the score and make up for Superman's superior strength. Superman, for his part, made a mental note that Dante had many demonic weapons and powers that could seriously harm Superman. Regardless, the two parted on friendly terms, with Superman telling Dante that he could call him Clark, and Dante giving Superman the phone number of the Devil May Cry, saying he could call him if he ever needed help with anything. Superman accepted gladly, pleased that he now had a new ally, even if he was slightly uneasy that Dante had actually been able to damage him, and he got the impression that Dante had been as non-serious as he had been.

Superman could have hit a lot harder, and could fly a lot faster, but he had the impression Dante also had hidden abilities. It didn't bother him too much. Dante could have killed him with the sword, or at least severely harmed him, and had chosen not to. Clark was actually quite pleased with the events of the day.
"I'll see you around, Dante."

Analysis:

This fight took place with neither fighting seriously. In that situation, the magic weakness of Superman will render him more vulnerable to Dante's magic blade than Dante is to Superman's non-serious punches. In the event both fight seriously, Superman has strength and faster than light speed which will obviously cause his punches to hurt Dante a lot. Superman undeniably has the edge in strength.

At the same time, Dante has the ability to slow down time, not that it means much. If Dante fights completely seriously, that would mean using his demon form, which in fact only has two canon events in which it is used in a fight. In one, the fight with Abigail, the fight ended the instant Dante transformed, making Devil Trigger capable of stomping Abigail, who was affecting the planet with his magic, and was distorting two worlds at once, albeit on a small scale. Not very impressive, obviously, but then we go to the main fight. In Dante's fight with Mundus, the only event in which Dante fought seriously at full power, Dante's devil form displayed faster than light speed, since there were stars all around him, and when he flew upwards, towards the stars that were above him, they were gone a second later when he stopped, the only logical explanation being that he flew past them. That indicates that Dante's Devil Trigger could in fact keep pace with Superman.

Mundus also displayed an ability to create dimensions using reality warping, and the stars and the faster than light feats displayed by both Dante and Mundus indicate the dimension was at least galaxy sized. That puts Mundus fairly high up, though obviously a bug compared to beings like the Presence and the Spectre. Dante's strongest form took hits from Mundus, so it makes sense that while Superman will still be able to damage him a lot, he won't kill him in one hit.

With that, it falls to comparable speed, with Superman still being a million times stronger. With the magic advantage Dante has, and his feat of besting Mundus in his strongest form, it fits that his magic attacks and demon blade can damage Superman more easily than Superman's fists will damage Dante. Put simply, this is actually a close fight on both sides. Dante gains a small advantage by virtue of greater skill and magic attacks.