DISCLAIMER: I do not own Justice League or Dragon Ball Z, or Dragon Ball GT.
Clark Kent sat in a small café with Lois, each drinking coffee. Clark was relaxed now that Luthor was in prison, and he was glad that his fight with Goku had done no serious damage. Despite the damage Goku had suffered, he was walking around already. Wonder Woman had been hurt too, but she was okay. Her hand had been broken, but it was already in the process of mending.
Clark's super hearing detected a snarling sound, which came from an object heading right for Clark. Clark quickly pulled Lois to her feet and ran around the corner, rapidly changing into his Superman costume. He looked up as a man who looked a bit like Goku, only shorter and much nastier looking, landed in the middle of the café, smashing several tables.
Vegeta stormed over to Superman, gripping him by the neck and attempting, unsuccessfully, to pull him forward.
"You! You're the one who defeated Kakarot. I am Vegeta, Prince of all Saiyans. Your opponent, and your inevitable defeat!"
Superman pulled Vegeta off himself, stepping back.
"If you want to do this, fine, but at least show some decency and take this fight somewhere unpopulated."
Vegeta punched Superman in the face, but hurt his fist, while Superman didn't even feel it. Snarling, Vegeta powered up to Super Saiyan 2, skipping the basic Super Saiyan state entirely. Vegeta slammed his fist into Superman again, and this time, Superman grunted slightly.
Vegeta screamed with rage, powering up to the animalistic Super Saiyan 4 state. Vegeta, now looking more ape than human, charged Superman, flinging punches at him. Superman was hit by several of the punches, and was staggered slightly by the surprising aggression. Vegeta then fired a charged Ki blast into Superman, launching him back several hundred feet. Charging after Superman, Vegeta fired a series of Ki explosions into Superman at close range, seeing Superman clearly hurt by it.
Vegeta then kicked Superman in the face, knocking him back a few paces, before firing a Galick Gun into him, launching him onto the ground. Vegeta then fired a Ki blast along the ground, sending Superman sliding across the city.
"Too easy. Kakarot must be getting soft in his old age."
As Vegeta started to move after Superman, a blast of red laser energy slammed into his left shoulder, burning him so deeply that he doubted the arm would properly function for several weeks. Superman then came flying back, slamming into Vegeta and simply collecting him. Superman flew straight through the atmosphere and through space, before dropping Vegeta at the Fortress of Solitude.
Vegeta stood, ready to fight with his remaining fully functional arm. Superman floated forward, not even bruised.
"You really want to do this? You should quit while you can."
Vegeta fired a Ki blast all over Superman, watching in annoyance as Superman staggered back one step. Superman then flew into Vegeta, throwing him onto the floor of the Fortress of Solitude. Vegeta planted his hands on Superman's chest, releasing an explosion of Ki which blew Superman to the other end of the Fortress.
Rising to his feet, Vegeta fired a finger centred blast of Ki at Superman, while Superman fired his Heat Vision at Vegeta. The purple beam and the red beam collided, before both exploded. Superman and Vegeta then charged, slamming into each other. Vegeta attempted to blast Superman with his close range Ki explosion, but Superman gripped his wrists, keeping the Saiyan's hands off himself.
Vegeta and Superman briefly struggled, before Superman threw Vegeta onto the floor, before punching him straight up through the roof of the Fortress. Superman then flew after Vegeta, punching him again, this time towards the Sun. Vegeta stabilised himself, firing a blast of Ki at the charging Superman, who flew straight through it, coming out the other side without a scratch, before slamming into the badly bruised Vegeta, punching him repeatedly, though he had calmed himself and was now holding back.
Finally Superman slammed his fist onto the top of Vegeta's head, launching him down towards the Earth. Superman then swooped down and caught the falling Vegeta, landing on the ground with the Saiyan Prince over his shoulder.
Superman and Goku lay Vegeta down in a spare room of the Watchtower, Superman having already scanned him and verified that nothing was broken. Goku turned to Superman.
"He challenged you, huh? Vegeta's like that sometimes. You were right not to hold back. Vegeta never does."
Superman shook his head.
"I did hold back, Goku. Just because you survived my proper hits doesn't mean he could. If I hadn't held back, he'd be dead."
Reasons for this outcome:
1. Superman's physical strength is astronomically greater than Vegeta's, as well as his speed being similarly greater, and unlike Goku, Vegeta doesn't have Instant Transmission to make up for the difference in speed.
2. Vegeta's Ki attacks may destroy planets, but that doesn't at all mean they could destroy Superman. Planets breaking from Ki attacks has an easy scientific explanation. The Ki can blast through the rock that makes up the planet surface, and though the planet gets more solid toward the centre, Ki beams actually gain power over distance rather than losing it. That would make it easy for the Ki beam to reach the core, and then it can blow the core apart. How else do you explain a small energy beam destroying a planet? If it merely exploded on the surface, then the planet would be destroyed every time a large Ki blast is used. Characters are regularly shown firing Ki blasts that hit other characters who are standing on the planet. If the explosion on the surface was adequate to destroy the planet, the Earth would have been destroyed in every single battle that took place on it during the series.